Forecasters predicted it would head toward land but later change direction, skirt the coast and head out to sea.
Mexico issued a tropical storm watch for a 240-mile stretch of coast from Punta Maldonado to Zihuatanejo, the U.S. National Hurricane Center in Miami reported.
Tropical Storm Aletta had winds of about 40 mph and was expected to reach wind speeds as high as 60 mph. Forecasters were predicting heavy rainfall to the Mexican coast.
The storm was moving north at about 7 mph, but forecasters did not expect it to reach the coast before turning back out to sea.