Left-hander Cristopher Sanchez was named the 27th man for Sunday's home doubleheader against the New York Mets and replaced Eflin as the starter in Game 2, a 6-1 loss to the Mets. Sanchez went 2 1/3 innings, allowing two hits and two earned runs.
The Phillies recalled right-hander Connor Brogdon from Triple-A Lehigh Valley and right-hander Francisco Morales from Double-A Reading in corresponding transactions.
The Phillies left for a seven-game road trip to Seattle and Los Angeles following Sunday's doubleheader. Neither Wheeler nor Eflin traveled with the Phillies to Seattle, but manager Joe Girardi said he is holding out hope one or both can eventually rejoin the team at some point on the road trip.
"We'll figure it out," Girardi told reporters. "One of them could be back. We've just got to wait and see what happens."
Wheeler, 31, is 1-3 with a 4.10 ERA through five starts this season. He made the All-Star team in 2021 and was runner-up in the National League Cy Young Award voting after finishing 14-10 with a 2.78 ERA and a league-leading 247 strikeouts.
Eflin, 28, is 1-2 with a 4.50 ERA through five starts in his seventh season with the Phillies.
Sanchez, 25, is 0-0 with a 5.40 ERA in four appearances this season. He has given up six runs on eight hits and five walks with 10 strikeouts in 10 innings.
Brogdon, 27, has made three relief appearances this season for the Phillies, allowing two runs on four hits in two innings. He has a 1.35 ERA with two saves in seven games for Lehigh Valley.
Morales, 22, is 1-0 with a 0.55 ERA with 28 strikeouts in 16 1/3 innings in nine relief appearances at Reading. He has yet to make his major league debut.
Reuters contributed to this report.