All that remained of Barbara was a weakening tropical low over southeastern Mexico, following the storm's landfall from the Pacific Ocean on Wednesday. The storm unleashed flooding rain and damaging winds.
In its wake, Barbara left at least two people dead, including one American, the AP website said on Thursday.
Fourteen fishermen were missing, having set out to sea from the town of Tapanatepec, Oaxaca, state civil defense director Manuel Maza Sanchez said.
A Mexican man drowned while trying to cross a rain-swollen stream in Pinotepa Nacional.
The American man was surfing at Playa Azul, a beach near Puerto Escondido, Sanchez said. Puerto Escondido lies about 120 miles west of the storm's landfall. Waves raised by the hurricane were to blame for the incident, he indicated.
The worst of Barbara's damaging wind and flooding rain passed east of Salina Cruz, site of Mexico's biggest oil refinery.
Rainfall was extreme, at least in some areas along the storm's path. Rainfall was about 17 inches within 24 hours at Arriaga, Chiapas state, according to weather data available to AccuWeather.com.
Barbara landed as a Category 1 hurricane, having 75-mph top sustained winds, at midafternoon Wednesday in southeastern Oaxaca state, Mexico, along the Gulf of Tehuantepec. Weakening followed quickly, owing to the region's rugged landscape, and winds had lowered to 50 mph by Wednesday night.
Barbara's landfall was unusual, inasmuch as it was the most easterly landfall of a Pacific hurricane since 1966, when reliable record-keeping began, the AP website said. Southwestern Mexico normally bears the brunt of Pacific hurricane landfalls. Moreover, it was the second earliest landfall since 1966.
The remnant low of Barbara was forecast to loiter over the Gulf of Campeche and nearby southeastern Mexico through at least early next week. Although immediate redevelopment of a named tropical storm was not foreseen as of Thursday, the remains of Barbara were expected to form part of a wide swath of unsettled tropical weather, marked by outbreaks of torrential rain and local flooding, from southern Mexico to the northwestern Caribbean, even the Bahamas and South Florida.