Morrow struggled throughout early spring training, giving up 7 earned runs through just 8 innings pitched. On March 18, manager John Gibbons confirmed that Morrow would be the team's fifth starter, citing a need to give him more time to prepare for the regular season. After struggling to open the season, including a start on April 26 where he walked 8 Red Sox batters over 2⁄3 innings, Morrow was placed on the 15-day disabled list on May 3 with a sprained right index finger. Later that day his injury was determined to be a more severe torn tendon sheath in his right hand, and he was transferred to the 60-day DL. Morrow made his first rehab appearance on August 27 with the Dunedin Blue Jays, pitching one scoreless inning. He was activated from the 60-day DL and added to the Blue Jays active roster on September 1, 2014. On November 1, the Blue Jays declined Morrow's $10 million 2015 option, making him a free agent.
On December 16, 2014, Morrow signed a 1-year, $2.5 million contract with the San Diego Padres. He made 5 starts with the Padres in 2015, posting a 2.73 ERA and 23 strikeouts, before going on the disabled list with right shoulder inflammation in early May. He remained on the disabled list into August, when it was determined that he required season-ending surgery to correct a shoulder impingement. On December 17, Morrow signed a minor league contract with the Padres that included an invitation to spring training.