Michael Essien has been banned from playing in the Indonesian league after playing his debut game without a work permit.
The duo 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 admits 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".
Flouting immigration and work permit laws in Indonesia can attract fines up to about 500 million Indonesian Rupiahs ($38,000) and prison sentences up to five years.
Meanwhile, Persib Bandung manager Umuh Muchtar has accused the Professional Sports Agency, which reports to the government and monitors foreign players in the country, of going too far.
"That they (Essien and Cole) are here is a joy for us, they want to raise up Indonesia's name in the world," he said.
"Everybody knows that Essien is a world-class player, not an illegal immigrant."