The former Liverpool and Finland defender, 38, will be assisted by Under-19 coach Sasha Lewandowski after wholesale changes were made following a 2-0 defeat to Freiburg.
"With Hyypia and Lewandowski in charge, we want to turn things around and resume right away," sporting director Rudi Voeller said. "The team now has to step up and show some responsibility.
"Bayer are better than this and we must aim higher."
Hyypia retired from playing last summer in order to study for his coaching badges at Bayer, who he joined from Liverpool in 2009.
He now has his UEFA A-license and feels he is ready to make the step into management.
"I know the team and firmly believe in it," he said. "We - Sascha Lewandowski and I - want to show Bayer Leverkusen how to get back on track.
"It is an unsettled team that has not taken its chances in recent weeks. But, having been at the club for the past three years, I have an advantage in that I know the players."
Dutt’s assistants Damir Buric and Mark Langner were also sacked after Bayer – who almost won the Bundesliga last season under Jupp Heynckes – all-but gave up on Champions League football, lying 11 points behind fourth-placed Borussia Moenchengladbach with six games remaining.
Gladbach can extend that lead to 14 points if they win at Hannover later on Sunday.