Martin (3-1) picked up the win Tuesday, walking one and striking out one in a scoreless ninth inning during Boston's 6-5 extra-inning victory over Toronto.
Red Sox manager Alex Cora said Sunday that he will "mix and match" at closer with Martin and Justin Slaten following the injury to Kenley Jansen (shoulder), Gabrielle Starr of the Boston Herald reports.
Martin (illness) made relief appearances Wednesday against the Orioles and Thursday against the Yankees, tossing a pair of scoreless innings and striking out three batters while giving up one hit and no walks.
Red Sox manager Alex Cora said Martin was unavailable Sunday against the White Sox since the reliever was feeling under the weather, Mac Cerullo of the Boston Herald reports.
Martin allowed four runs on four hits while striking out two over one inning in Tuesday's 7-2 loss to the Mets.
Martin earned the save in Tuesday's 4-1 win over Houston, working around a hit in a scoreless ninth inning. He struck out one.
The Red Sox reinstated Martin (elbow) from the 15-day injured list Wednesday, Chris Cotillo of MassLive.com reports.
Manager Alex Cora said Sunday that Martin (elbow) could be instated from the 15-day injured list Wednesday rather than being sent on a rehab assignment, Jen McCaffrey of The Athletic reports.
Martin (elbow) threw 35 pitches in the bullpen Saturday, Peter Abraham of The Boston Globe reports.
Martin (elbow) is on pace to return during Boston's upcoming series against the Astros, Ian Browne of MLB.com reports.