Hourihane is a club legend at Oakwell, having scored 31 goals in 135 appearances in his first spell at the club and captained them to an EFL Trophy and League One promotion double in 2016.
He won 36 caps for the Republic of Ireland during his career and returned to Barnsley as a player-coach under Clarke in the summer of 2024, but only played two games before deciding to hang up his boots.
"I am incredibly grateful to the club for giving me the opportunity to begin my management journey, particularly at a club that means so much to me," he said.
"Following discussions between the club and myself, we both felt that a change in the summer would be best to ensure a smooth transition.
"The main focus now is on the final five games and finishing the season as strongly as possible to provide the best platform going forward."
Hourihane's final game in charge will be a home fixture against Stockport County on 2 May.
Barnsley are currently in their fourth successive season in the third tier of English football, and reached the play-offs in 2023 and 2024.
The club announced a net loss of more than £6.5m, external for the 12 months ended in June 2025.
They will now begin the search for their seventh head coach since Valerien Ismael left in the summer of 2021 after guiding them to the Championship play-offs, the closest they have come to a return to the Premier League since their single top-flight season in 1997-98.
