Elon Musk’s swagger has helped win admirers and embolden Tesla Inc. TSLA -5.55% investors. This time, the billionaire chief executive may have gone too far.

On Thursday, Tesla’s shares fell 5.6%, erasing about $3 billion in market value a day after Mr. Musk sparred with Wall Street analysts in a show of defiance rare for traditionally staid conference calls to discuss a company’s quarterly results.

Several analysts reconsidered their outlooks for the Silicon Valley auto maker struggling to take on the century-old automotive industry.

Chief executives of publicly traded companies typically grit their teeth and coolly dance around pointed questions during these calls. Mr. Musk chose instead to dismiss analysts over their “boring, bonehead” questions, cutting off two of them when they asked about Tesla’s capital requirements and customer reservations for the Model 3 sedan.

“This is a financial analyst call—this is not a TED talk,” Toni Sacconaghi, an analyst with Sanford C. Bernstein & Co., said on CNBC Thursday after he was cut off by Mr. Musk on the call. “So when financial questions are asked, they should be addressed.”

In some ways, the combativeness was classic Elon Musk. The billionaire entrepreneur has made defiance of convention his calling card in a relentless pursuit to upend transportation, and in his eyes, save the world with driverless electric cars and rocket launches to Mars. He fires off Twitter posts at late hours rebutting critics who he believes get in the way, and he often makes grandiose statements about the future of technology.

Mr. Musk’s bravado has polarized investors, pitting short sellers who are sure Tesla is headed for demise, against the “longs” who believe his vision will win out. The backers have so far prevailed, giving Mr. Musk room to make, and sometimes miss, overly ambitious goals and lifting Tesla’s market value to rival those of General Motors Co. and Ford Motor Co. , much larger auto makers.

But even for Mr. Musk, the impertinent answers to analysts from big banks was jarring, and raised questions whether he was masking Tesla’s problems. On the call, he seemed more eager to talk about the future of Tesla—self-driving cars or the next electric vehicle—than the state of the business after the Silicon Valley auto maker burned through about $1 billion during the first quarter as production struggles continued to beset the Model 3 sedan.

Following the call, which was broadcast for investors online, analysts sent notes to clients that characterized Mr. Musk’s exchange as “bizarre theatrics” and “odd,” and said Mr. Musk might have struck some as being “dismissive” and “unhinged.” At least three analysts dropped their price targets.

Late Wednesday, while Mr. Musk began deflecting questions on the call, Tesla’s stock fell more than 5% in about a 20-minute span during after-hours trading.

Mr. Musk’s frustration bubbled up about a half-hour into the call when Mr. Sacconaghi asked about Tesla’s target date for achieving 25% gross margins on the Model 3—which, the analyst said, the company seemed to have pushed back by six to nine months from the goal stated just last quarter.

Chief Financial Officer Deepak Ahuja attributed the delay, in part, to added labor costs and a weak dollar. Mr. Musk interrupted to say the gross-margin difference is a matter of three to five percentage points and will be resolved in three to six months.

“Don’t make a federal case out of it,” he said.

Mr. Sacconaghi, who co-wrote a report last month questioning Tesla’s ability to automate its factory, then turned to the company’s investment plans. Tesla had previously said it expected spending this year to about match last year’s $3.4 billion, but on Wednesday announced it was scaling back plans to less than $3 billion, which could ease its cash crunch.

When Mr. Sacconaghi asked what the company’s specific capital requirements would be, Mr. Musk cut him off.

“Boring, bonehead questions are not cool—next,” Mr. Musk said, turning to the operator for the next question.

Joseph Spak of RBC Capital Markets then asked what percentage of Model 3 reservation holders who have been invited to start configuring their orders have actually done so.

Mr. Musk was silent for about 15 seconds.

“We’re going to go to YouTube, sorry. These questions are so dry. They’re killing me,” Mr. Musk said. He directed the operator to take questions from Tesla investor Galileo Russell, whose HyperChange TV YouTube channel features a video titled “Why I Bought Tesla Today at $255/Share.”

Mr. Russell, who had campaigned to get on the call usually reserved for analysts, got more than 20 minutes from Mr. Musk. The first of his dozen or so questions: When will Tesla launch its own network of driverless cars?

“Thank you for an interesting question,” Mr. Musk replied.

Following the call, Mr. Spak lowered his price target to $280 from $305, telling clients the “performance shook confidence” on the part of investors “which we’d argue is an important piece of the Tesla story.” The stock closed Thursday at $284.45. Mr. Sacconaghi kept his price target intact, writing that “beneath the bizarre theatrics” he considered Tesla’s quarter to be within analysts’ expectations.

When Wednesday’s call started, Tesla’s stock was down less than 1% in after-hours trading. Mr. Musk spent the first 10 minutes describing some of the challenges of ramping up auto production, such as robots’ struggles to put fiberglass mats atop of battery packs.

Analysts then began peppering Mr. Musk and Mr. Ahuja with tough questions about the Model 3 delays. Mr. Musk has directed the factory to run 24 hours a day, seven days a week, to reach the goal of making 5,000 of the sedans a week by around the end of the second quarter.

Brian Johnson, an analyst for Barclays, posed questions about the math, finally concluding that Tesla has about one vehicle coming off the factory line every two minutes, compared with the industry average of one a minute. That, Mr. Johnson suggested, seemed to be at odds with Mr. Musk’s claim in February that his factory would outpace the industry, which he called slower than a “grandma with a walker.”

Later, Mr. Musk again praised Mr. Russell’s line of questioning as he asked about a range of topics including the company’s Model Y compact sport-utility vehicle, which has yet to begin production.

“Asking questions that are not boring,” Mr. Musk said.

—Ben Eisen contributed to this article.

Write to Tim Higgins at Tim.Higgins@WSJ.com