The Iron lost 2-1 to their local rivals in the first-round replay on Tuesday night and Laws has paid the price.
The 52-year-old, who first took charge of the club in 1997, returned to Glanford Park for a third spell as manager in October 2012 but could not prevent his side from dropping to the fourth tier in his first season back at the helm.
United sit 12th in the League Two table, two points off the play-off places but are without a win in their last five matches.
"A further statement will be made later in the day."
- Sports & Recreation
- Scunthorpe United