Downs suffered a fractured skull and is being cared for at St. Vincent's Hospital in Birmingham, Ala. His condition has improved, and he was visited by his family and fiancee, the report said.
The 24-year-old left-hander, starting for the Double-A Montgomery Biscuits, was struck on the left side of his head by a line drive in the fifth inning off the bat of Christian Marrero of Birmingham.
According to The Montgomery Advisor, Downs never lost consciousness and was taken by ambulance to the downtown-area hospital.
Downs, a fifth-round pick by the Cubs in the 2003 First-Year Player Draft, has never pitched in the Major Leagues and was acquired by the Rays on July 24, 2008. Downs pitched mostly for Class A Charlotte this year, going 12-4 with a 2.00 ERA in 20 games (19 starts).
Downs has been placed on the Minor League disabled list, and with the Minors season coming to an end in early September, he's likely out for the remainder of the year.
"It is scary," Rays manager Joe Maddon said.
"With the pitchers ... you want to have balance in your finish, you want to be in a good fielding position. Sometimes guys just aren't. They just never arrive at that point, or they don't take enough come-backers during the course of the year just to maintain that reaction. But it's such a freakish and flukish and unpredictable play. It's horrendous what happened."
Alden Gonzalez is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.