Roach was reportedly speeding away when his BMW car flipped over several times before landing in the 3Ws park.
The 25-year-old suffered a head injury and was taken to hospital, the Barbados Today online newspaper claimed.
Roach took to Twitter a few hours later after the accident to reveal that he was recovering and in good health.
"Sorry To Scare My Friends, Family And Fans But I'm Straight! Thanks For The Love! #BlessUp," he tweeted.
Roach has played 23 Tests and 61 one-dayers but has not appeared up for West Indies in nearly a year because of a shoulder injury.