Tesla Inc. said it would request shareholder approval at its annual meeting for an increase in the number of shares of the electric-car maker to enable a stock split, though it didn’t specify when such a split would take place or what the ratio of shares would be.

Tesla shares were up nearly 8% to $1,088 a share in Monday trading. The company typically holds its shareholder meeting in the fall.

Tesla is currently authorized to issue 2 billion shares. As of Jan. 31, the company had 1.03 billion shares outstanding.

The move comes after Amazon.com Inc. this month said it would split its stock 20-for-1. Google parent Alphabet Inc. said on Feb. 1 that it would enact a 20-for-1 stock split, giving shareholders 19 more shares for every one they own.

Stock splits change the stock price, not the total value of an investor’s holding, although they have a history of generating a short-term rally in a company’s stock price.

The proposal comes almost two years after Tesla enacted a 5-for-1 stock split as shares of the company run by Elon Musk rode to new heights. Tesla, at the time, said it was making the move “to make stock ownership more accessible to employees and investors.”

Tesla shares surged last year as the company’s vehicle deliveries rose strongly despite global supply-chain constraints, and its profit advanced, too. The rally has turned Mr. Musk into the world’s richest person, according to the Bloomberg Billionaires Index.

The stock is down around 4% this year amid wider market turmoil following Russia’s attack on Ukraine that began last month. Tesla shares are still up more than 60% over the past year, though.

Tesla’s stock-split announcement comes as the company is temporarily idling its factory in Shanghai amid wider Covid-19 lockdown measures in China. Mr. Musk on Monday also tweeted he has again tested positive for the virus.

Write to Will Feuer at will.feuer@wsj.com