Melvin said a doctor recommended Crisp get an epidural for his neck injury.
Crisp, 35, left a game last week after just three innings because of neck pain and has not played since May 19. Oakland placed him on the disabled list on May 23.
It was reported last week that Crisp was set to see a neck specialist and could be shut down for an extended period of time.
The outfielder started the season on the disabled list after undergoing arthroscopic surgery to remove a bone spur and chips in his right elbow. He made his season debut on May 6.
In 45 at-bats this season, Crisp is hitting .044 with seven walks and 10 strikeouts.
The A's are hosting the New York Yankees on Thursday.
- Molly Geary