Vizcaino was outrighted to Triple-A Omaha on Friday.
Vizcaino allowed two runs on a hit and two walks in one inning during Monday's loss to the Giants.
Vizcaino's contract was selected by the Royals on Monday.
Vizcaino signed a minor-league contract with the Royals on Thursday.
Vizcaino (undisclosed) struck out the side in a scoreless inning of relief Sunday in his return from Triple-A Syracuse's 7-day injured list.
Vizcaino (elbow) was reassigned to minor-league camp Sunday.
Vizcaino has been shut down for about a week due to soreness in his elbow, Tim Healey of Newsday reports.
Vizcaino has been able to hit 96 mph with his fastball this spring, Anthony DiComo of MLB.com reports. "He feels strong," Mets manager Luis Rojas said Sunday. "He wants to get out there. The breaking pitches, they've looked nasty in the bullpens."
Vizcaino signed a minor-league deal with the Mets on Wednesday, Tim Britton of The Athletic reports.
Vizcaino (shoulder) was traded from the Braves to the Mariners along with Jesse Biddle on Monday in exchange for Anthony Swarzak.