The 25-year-old has scooped the gong for his scintillating form in front of goal, having contributed 19 strikes in all competitions for the Reds so far this season.
Salah, who signed for the Merseyside outfit from Roma for around £34m in the summer, was also a key figure in Egypt qualifying for the 2018 World Cup in Russia.
"I'm very happy to win this award, it's a special feeling for me," the former Chelsea star told BBC Sport. "I'd like to thank everybody; my teammates and the people I work with.
"I am very happy here at the club, I've had a very good start here. Also the manager [Liverpool boss Jurgen Klopp] has helped me to settle into the team.
"Last season I had a very good season with Roma, so I need to thank my teammates [there] and also my teammates in the national team. The people I work with are very professional and I'm happy with them. [Now] I'd also like to win it next year."
The winner is currently the Premier League's top scorer with 13 goals.