Feliciano was originally picked in the 36th round of the 1997 Major League Baseball draft by the Los Angeles Dodgers as a draft-and-follow player. He signed in May and debuted as a professional with the short-season Yakima Bears that summer. He batted.305 with 26 RBI, and stole 34 bases in 44 attempts in 77 games, finishing four steals behind Northwest League leader Juan Pierre. Feliciano led the Northwest League in at-bats with 302, outfield putouts with 191, and outfield double plays. In, Feliciano played for the Advanced-A Vero Beach Dodgers and he stole 20 bases in 30 tries. He played for the Class-A AdvancedSan Bernardino Stampede in and batted.289, stealing 31 bases while being caught 11 times. He fielded.996, leading California League outfielders. Feliciano spent back at Vero Beach and hit.262, stealing 22 bases in 32 attempts. Feliciano again led his league's outfielders in fielding percentage, this time handling 284 chances without an error. Feliciano struggled in playing for the Jacksonville Suns, only batting.237 in 100 games. He hit.300 that winter for the Cangrejeros de Santurce in the Puerto Rico Baseball League. He began even worse than he had done in the summer of '02, hitting.138 and 4 RBI in 37 games. He was released by Dodgers on May 29.
On June 7, 2010, the New York Mets selected the contract of the 31-year-old outfielder. He went to Puerto Rico to play against the Florida Marlins in a three-game series. He had been leading the International League in hitting with a batting average of.385. On July 12, he was demoted for the return of the injured Carlos Beltrán. On August 22, 2010, he was called up from the Triple-A Buffalo Bisons to take the place of Rod Barajas. When the Mets traded Jeff Francoeur to the Texas Rangers, Jesus was sent down to the Minors again to make room for rookie outfielder Lucas Duda. On November 5, 2010, Feliciano was sent down to the minors to the Triple-A Buffalo Bisons, then became a free agent after refusing the minor league assignment.
He was selected to play on the Puerto Rican national team for the 2009 World Baseball Classic, where he was the starting left fielder alongside major leaguers Carlos Beltrán and Alex Ríos.
Coaching career
He joined the Chicago Cubs organization after retiring and replaced Bill Buckner as hitting coach for the Boise Hawks in 2014. He was the hitting coach for the South Bend Cubs in 2015. He served as the Eugene Emeralds manager in 2016 and 2017. He led his club to the Northwest League championship in 2016 and won 2016 Northwest League Manager of the Year. He served as hitting coach for the Tennessee Smokies in 2018. Prior to the 2019 season, he was hired by the Los Angeles Angels as their first base and outfield coach.