"We're starting to get some guys moving, get them out of here and out playing and hopefully getting them back on the field as soon as possible," manager Mike Redmond said.
Heading into the season, Eovaldi was expected to be the No. 2 starter. But he and Henderson Alvarez were placed on the disabled list, both with shoulder inflammation, the day before the opener.
Pitchers can spend 30 days on rehab assignment, compared to 20 days for position players.
Alvarez threw 20 pitches off the mound on Tuesday, but he is at least three or four weeks -- if not longer -- away from returning.
Eovaldi could be back by the middle of June.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter