Both Essien and Cole joined Persib Bandung last month, a move hailed as giving the Indonesian giants as well as the league global appeal.
They made their league debut over the weekend in a goalless drawn game.
However, the government-backed Professional Sports Agency found the players did not have the required work permits to play in the Indonesia league and have therefore banned them until further notice.
"Today we gave a strong warning to Persib in the form of a letter saying that as long as Persib had not completed the permits, which should be issued by the manpower ministry, we are banning Essien and Cole from playing," said Maulia Purnamawati, the immigration chief in Bandung, the city where the club is based.
Persib Bandung admit that they knew Essien and Cole's permits weren't ready when they fielded them on Saturday, but claim they were given the go-ahead by the Indonesian Football Association.
Joko Driyono, the General Secretary of the Indonesia Football Association explained that they allowed the club to do so because the process to acquire the permits is "not easy nor fast".
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