A push to expand rent control in California is sending a chill through the state’s apartment industry, prompting more investors to sell properties or hold off on buying.

Ben Lamson, whose family owned just under 100 apartments in the Inland Empire area in southern California, said he has sold about 70 units and is in contract to sell the remaining ones. He is taking all the money and investing it in properties in the Las Vegas area, he said.

Mr....