As of Wednesday morning, Rina's maximum sustained winds were 110 mph -- just 1 mph short of Category 3 status, the Miami-based National Hurricane Center said.
The center of the storm was located about 230 miles (370 kilometers) south-southeast of Cozumel, Mexico, and about 205 miles (330 kilometers) east-southeast of Chetumal, Mexico, forecasters said. It was moving westward slowly, at about 4 mph (6 kph).
Forecast models show Rina strengthening into a Category 3 hurricane before approaching the Yucatan.
Rina "has the potential to become a major hurricane today or tonight," the Hurricane Center said Wednesday morning. Rina is forecast to reach Mexico's Yucatan Peninsula on Thursday.
No tourists had been evacuated from the state of Quintana Roo, which includes Cozumel and Cancun, as of Wednesday morning, said Juan Gabriel Granados, operation director for state civil protection. The state civil protection agency was meeting with emergency officials every six hours, he said.
"Our main concern is Cozumel and the Riviera Maya (the eastern coast of the Yucatan) because that's where the hurricane is expected to hit first," Granados said. "All of the authorities are under alert. The army, the Marines and the Quintana Roo state police are also under alert."
Water activities and fishing were canceled throughout the area, he said. Travel from the mainland to the island of Cozumel and back will be suspended beginning at 4 p.m. Wednesday.
Holbox Island, in northern Quintana Roo, was evacuated, he said, but did not say how many people were involved. Another 500 people were evacuated from Punta Allen, a fishing spot, and another 50 people were evacuated from another fishing spot, Punta Herreros.
Schools were canceled in six municipalities, including Benito Juarez, where Cancun is located. The city has a population of 750,000, Granados said, and the number of tourists in Quintana Roo presently is about 83,500.
Many of those in Cancun, residents and tourists alike, were stocking up on supplies to prepare for the storm.