Stone, 23, was stabbed outside a bar at 21st and K streets at 12:45 a.m. Thursday while out with four friends, ABC News affiliate KXTV reported.
"It is believed that the victim was out with a group of friends when a physical altercation led to the victim being stabbed multiple times in his upper body," Sacramento police said, adding that alcohol is believed to be a factor.
Surveillance video obtained in Spencer Stone fight, stabbing
He was taken to UC Davis Medical Center, where he is recovering from significant but non-life-threatening injuries.
Police said two assailants fled in a car. No immediate arrests were made.
"This incident is not related to terrorism in any way," Deputy Police Chief Ken Bernard said. "We know it's not related to what occurred in France months ago."
MORE: UCLA fraternity, sorority under fire for "Kanye Western" party
Bernard would not say what the fight was about and said there was no evidence Stone's assailants knew who he was. The deputy chief said he did not know whether Stone was drinking, but others in his group were.
Air Force spokesman Lt. Col. Christopher Karns said the incident remains under investigation by local law enforcement.
Stone, Oregon National Guardsman Alek Skarlatos and Anthony Sadler have become widely lauded figures and sudden celebrities, making appearances on late-night talk shows, receiving a congratulatory call from President Barack Obama and earning France's highest honor from President Francois Hollande.
MORE: Woman says eye was super glued shut by accident
The three subdued Ayoub El-Khazzani, a man with ties to radical Islam, who had boarded the train with a Kalashnikov, a pistol and a box cutter.
Stone, who has been acclaimed for his aggressive role in disarming the gunman, had undergone medical treatment at a military base in Germany for a lacerated thumb and other injuries he suffered in the attack. He is assigned to Travis Air Force Base in California.
Skarlatos, who appears on this season of "Dancing With the Stars," tweeted his support for the Stone family.
Everybody send prayers out to the stone family today— alek skarlatos (@alekskarlatos) October 8, 2015
ABC News and The Associated Press contributed to this report.