Salah was in irresistible form at the Vitality Stadium on Sunday (AEDT), opening the scoring and adding two more in an easy 4-0 Liverpool win, with Steve Cook also netting an own goal.
Unsurprisingly, Salah was named man of the match and handed the award at full-time, but he refused to take it, instead passing it on to Milner.
The former Manchester City, Leeds United and Aston Villa midfielder reached the milestone and Salah felt it necessary to honour such an achievement.
"I'm not taking it," Salah told Sky Sports.
"It's his [Milner's] 500th game
"He deserves it today, he's had an amazing career. I hope I have more games like this in my career, but I will not take it [the award]."
Salah's hat-trick took him on to 10 Premier League goals for the season, while Liverpool moved to the top of the table as Manchester City lost to Chelsea.