Luigi De Canio will take charge of the team for the final five matches of the campaign as part of the 18th managerial change in Serie A this season.
Malesani was only reappointed at the start of this month having been previously sacked in December.
Genoa were 4-0 down in their game against Siena at the Stadio Luigi Ferraris when some of the club's hardcore 'ultra' fans threw flares on to the pitch and took to the field, forcing the match to be suspended.
Some Genoa players removed their shirts in response to chants that they were not fit to wear them.
The match was eventually completed, with the defeat leaving Genoa just one place and one point above the relegation zone.