At its strongest, Bud should be a 115-mph Category 3 storm, the National Hurricane Center said.
Bud's center is now just over 300 miles south-southeast of Cabo San Lucas, Mexico, moving northwestward.
Forecasters said Bud was expected to strengthen further before a slow weakening trend starts Tuesday.
The second Eastern North Pacific hurricane of the season is whipping up 120 miles per hour winds but moving at a glacial pace of about 7 miles per hour. In addition, rain from Bud "could cause life-threatening flash floods and mudslides in higher terrain".
"Even though Bud is now a powerful hurricane, it is going to pass over ocean waters of progressively decreasing heat content", the center said.
Trump, Kim agree to work toward denuclearization
And they also agreed to work together to recover "POW/MIA remains", presumably American soldiers killed in the 1950-53 Korean War. Sanctions will remain until North Korea completely and verifiably eliminates its weapons of mass destruction programs, he added.
Map showing the path of Hurricane "Bud". That same climate pattern could also put a damper on the Atlantic hurricane season. Rainfall of 3 to 6 inches (75 to 150 millimetres), with isolated patches of 10 inches (250 millimetres), was possible over much of that region into Tuesday afternoon.
It's not unusual for the Eastern Pacific season's first storm to be a Category 4 hurricane.
The National Hurricane Center noted winds, heavy rain and unsafe ocean swells are likely.
A tropical storm watch was issued for the southwestern coast of Mexico from Manzanillo to Cabo Corrientes, popular resort areas.
And Bud will probably not be the last hurricane of the season, with AccuWeather meteorologists anticipating the East Pacific basin remaining active as an above-normal number of tropical cyclones remain in the forecast.