Muñiz made his major league debut on September 25, 2007. He threw 1.1 innings and gave up 2 earned runs.
Muñiz was called up to the Mets on May 27, 2008, to replace injured pitcher Matt Wise in the bullpen. He was then sent back down to the New Orleans Zephyrs, which was the Mets Triple-A affiliate prior to 2009. He was then recalled on June 25 when Claudio Vargas was designated for assignment.