The 32-year-old is accused of raping two women, as well as sexually assaulting a third.
The alleged offences took place between 2021 and 2022, when he was an Arsenal player.
Partey spoke at Southwark Crown Court to confirm his name, date of birth and his not guilty pleas.
The Ghana international was charged four days after leaving Arsenal following the expiry of his contract at the end of June.
He signed for Villarreal in August and appeared for the Spanish side in their 1-0 Champions League defeat to Tottenham in London on Tuesday.
Partey was brought on as a substitute in the 78th minute at the Tottenham Hotspur Stadium.
The midfielder joined Arsenal from Atletico Madrid in 2020 in a transfer worth around £45 million.
He appeared 52 times for the Gunners last season, scoring four goals. Overall, he played 167 games for the club, scoring nine times, and has also made more than 50 appearances for Ghana.
An Arsenal spokesperson previously said: "The player's contract ended on June 30th. Due to ongoing legal proceedings, the club is unable to comment on the case."