Murphy landed on the disabled list on June 5 with a strained left quadriceps.
General manager Sandy Alderson recently had identified Tuesday's series opener in Milwaukee as the target date for Murphy's return.
Murphy might be playing in minor league rehab games midweek.
He still has hurdles to clear in his rehab progression, particularly involving running.
Murphy is expected to return to the majors as a third baseman for the duration of David Wright's absence.