The storm was centered about 90 miles southeast of Cozumel island Monday afternoon with maximum sustained winds of 80 mph, the U.S. National Hurricane Center said.
A hurricane watch was posted from Morgan City, La. to the Mississippi-Alabama border. The Gulf Coast is still reeling from Hurricane Delta, which hit the region three weeks ago.
There are concerns that remaining debris from Delta could become projectiles when Zeta is expected to make landfall sometime this week. Local authorities are taking the storm seriously, but with a distinctly less alarmed tone than when Delta strengthened to a Category 4 storm off the coast. Zeta is currently classified as a Category 1.
Zeta broke the record for the previous earliest 27th Atlantic named storm that formed Nov. 29, 2005, Klotzbach said. It's also the 11th hurricane of the season.
On average, six hurricanes and 12 named storms occur each hurricane season.
The Associated Press contributed to this report.