Aquilani's last game in charge was Saturday's 3-0 loss at AS Roma, the club where he began his playing career.
The 42-year-old former Liverpool player and Italy international was appointed Sassuolo manager in June, having played for the club in 2017.
Aquilani won two of his first four league games in charge, but since then his side have gone seven matches without a win, losing six.
Sassuolo are 17th in the standings on eight points, one ahead of Monza. They have the worst defensive record in the top flight, conceding 29 goals in 11 games.
Their next game, after the international break, is a home match against Genoa on November 22.