Morański underwent surgery at the 5th Military Clinical Hospital in Kraków.
The procedure involved examining and cleaning his wounds and stabilising his elbow.
Paweł Maleta, head of the hospital's reconstructive orthopaedic surgery department, said it was preparation for further operations, with at least one more planned.
Maleta said the officer's condition was stable but serious, mainly because of a chest injury that had previously been treated at Kraków's Gabriel Narutowicz Specialist Municipal Hospital.
Morański also faces multi-stage reconstructive treatment for his severely damaged arm.
"The patient was woken up immediately after the procedure, which also indicates that his condition was good enough for the anaesthetists to allow it," Maleta said.
He said at least one major operation and possibly several smaller procedures were still ahead, making rest and recovery between surgeries important.
Maleta said doctors hoped the treatment would allow Morański to regain the best possible function of his injured limb.
If treatment of the chest wound and the arm continue successfully, he will probably remain at the military hospital until he recovers, doctors said.
Hospital director Bartłomiej Guzik said giving Morański "peace and quiet" was essential to his recovery, full recovery of his physical abilities and eventual return to police service.
He said the hospital's aim was to make that possible.
Guzik said the initial life-saving operations had brought significant progress, while the current stage involved long, painstaking hours of work. He added that the officer faced a lengthy recovery.
Morański intervened alongside his patrol partner Jakub Kulik on Saturday against an armed attacker who was shooting at random people in Kraków's Main Market Square. Both officers were shot and taken to hospital.
(sp)
Source: PAP