After shooting Ortiz, he was apprehended and beaten by a crowd at the bar.
The Red Sox issued a statement on Tuesday morning on behalf of David Ortiz's wife, Tiffany, with an update on Big Papi's recovery. "On behalf of me and my family, I want to thank John and Linda Henry, Tom Werner, Sam Kennedy and the Boston Red Sox for all that they are doing for David and our family, as well as Dr. Larry Ronan and the fantastic staff at Massachusetts General Hospital".
Leo Ortiz added: "Big Papi will be around for a long time".
Tiffany did not speak on that.
In the U.S., fans prayed for his recovery and wished him well, with New England Patriots star Julian Edelman assuring him on Instagram: "Papi, all of New England has your back".
Ortiz, 43, had been airlifted to Boston Monday night on a medical air ambulance chartered by the Red Sox.
A man who allegedly confessed to playing a role in the shooting was identified by police as 25-year-old Eddy Feliz Garcia. The bullet exited Ortiz's stomach.
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He was arrested on the way to the airport and later sentenced to 10 years behind bars on espionage charges in a closed-door trial. Authorities accused him of being an American spy, allegations vigorously rejected by his family and associates.
While Ortiz's representative, Leo Lopez, denied the claims that Ortiz was having an affair, he did say that the shooting appeared to be the work of "hired killers." He was treated at a local hospital before being released into police custody. She also expressed appreciation to Dr. Larry Ronan and his staff at Massachusetts General for caring for Ortiz.
Police have not yet released the identity of the suspected gunman.
He was hailed as a hero in Boston for rallying the city after the Boston Marathon bombing.
Another one of Ortiz's former Red Sox teammates, Hall of Fame pitcher Pedro Martinez, who also hails from the Dominican Republic, broke down in tears while talking about Ortiz on Monday night during a broadcast on the MLB Network.
The Red Sox offered "all available resources" to help him recover and sent an aircraft to bring him back to Boston.
The Red Sox held a moment of prayer for Ortiz prior to their home game Monday night against the Texas Rangers.
Ortiz made 10 All-Star teams and won three World Series with the Red Sox before retiring in 2016.