Koeman was dismissed on Wednesday night, following a 1-0 loss to Rayo Vallecano in LaLiga, which leaves the club in ninth place.
The defeat came days after a 2-1 reverse against Real Madrid in El Clasico.
Xavi Hernandez is widely expected to eventually take charge of his former club.
The former Spain midfielder has impressed with Al Sadd in Qatar since 2017, accumulating seven titles.
However, Barjuan will be in the dugout when Barcelona take on Alaves this weekend.
A Barcelona statement read: “His interim position as first team head coach shall end as soon as the club has hired a full-time head coach to replace the dismissed Ronald Koeman.
“FC Barcelona president, Joan Laporta, shall be officially introducing Sergi Barjuan to the first team squad this afternoon before the training session at the Ciutat Esportiva.”