"He was lying on the ground and we ran over in zig-zag fashion," Mikail Ozen, a personal trainer and mixed martial arts fighter, told journalists, pointing to the place he and his friend Recep Tayyip Gultekin said the police officer had lain.
He said two other police officers, who threw themselves onto the injured officer to protect him, urged them to stay back for their own safety during what Austria's government described as an Islamist terrorist attack in which four people were killed.
But he said they walked over and helped carry the injured officer to an ambulance.
"They were shocked, and we were shocked ... The paramedics were standing over there ... We looked at each other and we just walked over. We did what was necessary," he said.
"I, as a Muslim of Turkish descent, want to say: I live in Austria, I was born in Austria, I went to school in Austria and learned my profession here in Austria," Ozen said. "If the same thing were to happen again today, I would do the exact same thing without a second thought. Because we live in Austria, we stand with Austria."
Austrian Interior Minister Karl Nehammer at a news conference said: "It's important for me to mention that the injured police officer was brought to safety by two Austrians with an immigration background." He did not name them.
Vienna police were not immediately available for comment.
Earlier, Gultekin told Turkish state-owned Anadolu news agency that he and Ozen had been in Vienna city center when they heard gunshots, headed in the direction of the noise and saw a gunman shooting a passerby.
"After I carried the wounded woman to a nearby restaurant, the terrorist pointed his gun at me," Gultekin said, adding he threw himself to the ground and was lightly hurt in the leg.
"We got into my friend's car and went to the nearest police station to report the incident," he said.
Gultekin said they also helped an elderly woman move to a safe location.
The men's actions drew praise from Turkish Foreign Minister Mevlut Cavusoglu, whose country's relations with Austria have been strained in recent years.
"Last night there were two heroes in #Vienna. Recep Tayyip and Mikail did what a true Turk and Muslim is expected to do! Thank you young men. WE ARE PROUD OF YOU!" he wrote on Twitter.He later told a news conference he had spoken with his Austrian counterpart to convey Ankara's condolences and repeated his praise for the men, saying they had disregarded risks to their own lives to help victims.