The move was made retroactive to June 9.
Eovaldi is 4-2 with a 3.16 ERA and 72 strikeouts in 12 starts this season. The right-hander hasn't allowed a run in his past two starts, including on Wednesday night when he pitched five innings, allowing six hits and striking out five in Boston's 1-0 victory over the Los Angeles Angels.
He is the second member of the Red Sox's rotation to be placed on the injured list in recent days. On Friday, the team placed right-hander Garrett Whitlock on the 15-day injured list because of inflammation of his right hip. That move also was made retroactive to June 9.
Boston had already altered its rotation to give Eovaldi more recovery time before his next turn. The Red Sox will start Nick Pivetta for Tuesday's series opener against Oakland.
Right-hander Kutter Crawford, who was recalled from Triple-A Worcester on Sunday to fill the open spot on the Red Sox's major league roster, pitched five scoreless innings in the Red Sox's 2-0 victory over the Seattle Mariners on Sunday. He struck out seven but also walked four, keeping Seattle hitless until Luis Torrens lined a single with two outs in the fifth.
The Associated Press contributed to this report.