The 59-year-old Scasny, who led Sparta to the Europa League quarter-finals last season, was ditched following a series of poor results, culminating with Sunday's 2-0 home loss to arch-rivals Slavia Prague.
His three assistants will act as interim coaches, Sparta said.
Sparta host Inter on Thursday two weeks after a 3-0 loss in their opening Group K encounter at Southampton.
It's a must-win game for both sides after Inter were stunned 2-0 at home by Israeli minnows Hapoel Beer-Sheva in their opener.
Sparta, who have won 36 Czechoslovak and Czech league titles - the last one in 2014 - sit fourth in the league after eight rounds, trailing leaders FC Zlin by five points.