Martinez's 78-year-old father, Pablo, has a form of brain cancer.
Wilson said the team does not know how long Pedro Martinez plans to remain in the Dominican Republic.
The Mets had hoped Martinez could return before the end of the month, possibly for a series against the Los Angeles Dodgers from May 29-31. The 36-year-old has been on the disabled list since April 2 with a strained left hamstring.