Green doesn't believe the injury will land him on the DL, which is a good thing, because the Angels don't really have anybody else.
"We've got some guys banged up at inopportune times right now," Angels manager Mike Scioscia said.
Specifics of Giavotella's illness weren't revealed, but it isn't considered serious.
Giavotella missed the entire three-game weekend series against the Blue Jays with the ailment and was away from the team Friday and Saturday. The 28-year-old stopped by the Angels' clubhouse Sunday, but wasn't available to play.
"It's going to take me a couple more days to get back," he said. "But I'm feeling good again, getting my strength back up, and after a few days I should be fine."
Giavotella was acquired from the Royals for journeyman reliever Brian Broderick in the middle of December, then won the starting job in Spring Training and became a pleasant surprise offensively, sporting a .265/.312/.350 slash line in 469 plate appearances.
Now, his absence is crippling to a lineup that has baseball's lowest OPS for August.
Giavotella won't be eligible to return until Sept. 5. Until then -- and perhaps beyond that -- the Angels are hoping Green can be their everyday second baseman. Green, 27, is 7-for-29 in the Majors this season but has been solid, as usual, in the Minor Leagues, sporting a .306/.337/.449 slash line in 414 plate appearances for Triple-A Salt Lake.
• The Angels called up right-hander Drew Rucinski from Triple-A Salt Lake to take Giavotella's spot on the roster. Rucinski was brought up to provide length for a bullpen that absorbed 20 1/3 innings over its last four games, from Thursday to Sunday.
• David Freese (fractured right index finger) is expected to play third base for Salt Lake within the next three or four days, Scioscia said. That could put Freese on track to rejoin the Angels at some point before the end of their road trip, on Sept. 2.
• Fellow third baseman Conor Gillaspie recently cleared waivers and was outrighted to Salt Lake. Gillaspie, designated for assignment last Aug. 18, will have to be added to the 40-man roster in order to rejoin the team when rosters expand next Tuesday.
• Cory Rasmus (right forearm strain) has been playing catch from 90 feet and could be nearing his return. Rasmus is eligible to be activated off the DL on Monday and could return then, or perhaps when rosters expand.