Former Cheltenham boss Yates, 46, replaced John Gregory as Reds manager on a two-year deal in May 2015, but won only 13 of his 47 games in charge.
Crawley were bought by businessman Ziya Eren in March, who targeted reaching the Championship in eight to 10 years.
"The recent form and performance of the team suggests change is needed," a club statement said.
"The board will be interviewing potential candidates in the next few days to make the right appointment to move the club forward.
"The days and weeks ahead will determine the right path for the club."
Crawley's recent poor run of form has seen them slide to 18th in the table, but they are 12 points clear of the relegation zone with two games left to play this season.
Crawley Town have parted company with manager Mark Yates and assistant Jimmy Dack following six successive defeats.