The 29-year-old was driving a pickup truck when he crashed against a wall late Wednesday along a road southwest of the capital of Santo Domingo.
"We've talked with Pedro's family, and they've told us he's doing well and resting at home," Juan Mercado, general assistant manager of the Cibao Giants winter league team, told The Associated Press.
The cause of the crash is not clear. Strop was traveling with a friend identified as Yeudy Delgado, who also was not injured, officials said.
Strop was 2-4 with a 2.21 ERA and two saves last season after joining the Cubs in a midseason trade in 2013. He's a six-year veteran having played for the Texas Rangers and Baltimore Orioles before being traded with Jake Arrieta to the Cubs for pitcher Scott Feldman.
It was the third crash within a month involving a Dominican baseball player.
Ronald Guzman, a prospect with the Texas Rangers, was involved in a fatal accident on Tuesday in which a 27-year-old man died. On Oct. 26, St. Louis Cardinals rookie outfielder Oscar Taveras and his girlfriend died in a crash. Police said he was driving with a blood alcohol level more than five times the legal limit.
Several other players have died in the past two decades in car crashes in the Dominican Republic, which has the second-highest traffic-related death rate in the world, with nearly 42 deaths per 100,000 people.
ESPNChicago.com's Jesse Rogers and The Associated Press contributed to this report.