Tonkin was designated for assignment by the Mets on Friday, Anthony DiComo of MLB.com reports.
The transaction frees up a spot on the 26-man and 40-man rosters for Julio Teheran. Tonkin allowed eight runs (two earned) over four innings covering three relief appearances with the Mets. There would seem to be a good chance the 34-year-old passes through waivers unclaimed.