The storm was packing 110 mph winds early Wednesday morning and moving at 3 mph, according to the Miami-based National Hurricane Center. That is 1 mph away from a Category 3 hurricane.
Forecast models show Rina strengthening into a Category 3 hurricane before approaching the Yucatan. The projected path shows Rina back at Category 2 intensity when it takes aim at Cancun on Thursday.
Residents and worried travelers in Cancun stocked up on supplies Tuesday to prepare for the storm to hit the popular Mexican resort city.
Carla Bautista bought bread, water and canned tuna.
"It's my first hurricane. This is new. ... I'm a little afraid, because I don't know what to expect," said Bautista, 28, who moved to Cancun two months ago from Mexico City.
Mexican officials issued a hurricane warning for the east coast of the Yucatan Peninsula from north of Punta Gruesa to Cancun as the Category 2 storm strengthened. Similarly, U.S. officials issued a travel alert, advising U.S. citizens in the area to prepare themselves for the possibility of a hurricane.
Some tourists decided not to take any chances.
"We wanted to get out of there. ... We were on vacation and just didn't want to be stressed," said Kathy Davis, 57, an American with a timeshare in Cancun.
She said she and her husband celebrated their 25th wedding anniversary at the airport while waiting to catch a flight.
In Cancun's hotel area, crews were securing boats and clearing palm fronds and debris.
Kelly McLaughlin moved her 6-year-old son's toys inside and trimmed tree branches around her home.
"I'm just checking everything to make sure there's nothing loose," said McLaughlin, a Canadian who's lived in Cancun for eight years.
McLaughlin, 40, said preparing for storms has become routine since Hurricane Wilma devastated the area in 2005.
"My friends that are fairly new to Cancun are a lot more nervous and starting to get a little stressed," she said. "I'm just trying to keep everyone calm."
Lines at supermarkets and gas stations were long, residents said.
As of 2 a.m. ET Wednesday, the center of Rina was about 240 miles east-southeast of Chetumal, Mexico, and 250 miles southeast of Cozumel, Mexico. It was moving west at 3 mph, but was expected to gradually turn northwest and speed up over the next two days, forecasters said.