Peña signed with the New York Mets as an international free agent in 2007, receiving a $750,000 signing bonus. He made his professional debut with the Savannah Sand Gnats of the Class A South Atlantic League (SAL), where in 103 games, he hit .210 with five home runs, and 30 runs batted in (RBIs). Peña also spent the 2008 season with the Sand Gnats, where in 105 games, he hit .264 with six home runs, 41 RBIs, and 22 doubles. He was named to the SAL All-Star Game as a backup catcher to Jesús Montero. Peña played 2009 with the St. Lucie Mets of the Class A-Advanced Florida State League (FSL), where in 100 games, he hit .224 with eight home runs and 44 RBIs. He was named to the FSL All-Star Game as a backup catcher for Austin Romine. He missed most of 2010 with a broken foot. He made his debut on August 14 in a 10-game rehab assignment in the Gulf Coast League, and on August 26, he returned to St. Lucie, appearing in 10 more games. Peña played 2011 with St. Lucie, where in 95 games, he hit .223 with five home runs and 37 RBIs.

Peña began his fourth season with St. Lucie in 2012. In 41 games with St. Lucie, he hit .254 with four home runs and 22 RBIs. On June 21, he was promoted to the Binghamton Mets of the Class AA Eastern League, where in 40 games, he hit .198 with three home runs and 17 RBIs. He also threw out a career high 45% of would-be base stealers. Peña began 2013 with Binghamton, where he hit .246 in 21 games before earning a promotion to the Las Vegas 51s of the Class AAA Pacific Coast League on May 18. In 68 games with the 51s, he hit .257 with nine home runs and 39 RBIs. After the season, he became a minor league free agent.

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