Nine people were killed in the town of Yecuatla, three in the city of Tuxpan, and one in the town of Atzalan, all in Mexico's eastern Veracruz state, Governor Javier Duarte said.
Mr Duarte added: "All of the deaths were caused by landslides in the hills above their homes."
Officials said damage had affected 10% of major roads in Oaxaca although the bulk of oil and gas installations of state-run monopoly Pemex are located to the south of the once-powerful storm, and were not affected, a company spokesman said.
Located about 75 miles west-southwest of Tuxpan, the remains of Fernand had maximum sustained winds of 30mph and dissipated further inland at about 9mph, the US National Hurricane Centre said earlier on Monday.
Fernand made landfall near the coastal city of Veracruz early in the day.
More than 200 people had been evacuated from their homes in Veracruz state, according to local emergency services.
Mexico's government stopped all costal warnings earlier in the day.
Fernand was still expected to produce between four and 15 inches of rain in the east-central states of Veracruz, Hidalgo, Puebla and San Luis Potosi, as well as the northern state of Tamaulipas.
Fernand, which had started off as a tropical storm before weakening to a tropical depression, was the fifth named storm of this year's Atlantic hurricane season, which runs from June 1 to November 1.