Martinez (back) is expected to begin swinging a bat again Monday, and he should resume his minor-league assignment later this week, Tim Britton of The Athletic reports.
The veteran designated hitter hasn't played for Single-A St. Lucie since April 6 due to back tightness, and he received an injection Tuesday to speed his recovery. Assuming he gets back into the St. Lucie lineup this week, Martinez could be in line to make his Mets debut before the end of the month.