Manager Alex Cora said the surgery went well, and the Red Sox said in a statement that Eovaldi "is expected to make a full return to pitching within six weeks."
When Eovaldi had similar surgery last season while with the Tampa Bay Rays, he missed two months.
The Red Sox placed Eovaldi, 29, on the injured list Saturday. He said he didn't experience any symptoms after his start against the New York Yankees last Wednesday, when he pitched six innings while allowing one unearned run, walking one and striking out six.
Eovaldi knew something was wrong when he could not straighten out his arm during the team's off day in Tampa Bay.
Eovaldi signed a four-year, $68 million deal in December. He is 3-3 with a 4.08 ERA in parts of two seasons in Boston. So far this year, the hard-throwing righty has a 6.00 ERA in four starts, allowing 14 runs in 21 innings pitched, striking out 16 and walking 11.