The pilot is believed to have made it as far as the cockpit before he was replaced by another captain when many passengers staged a walk off, the Jakarta Post reports.
The travellers were reportedly alerted to his alleged state of intoxication when he made an incoherent flight announcement while preparing for take off.
A passenger has posted a video of the alleged incoherent announcement online which shows people onboard the plane looking confused.
The 1 hour 20 minute flight was due to take off from Juanda International Airport in Surabaya, East Java, and was bound for Soekarno Hatta International Airport in Jakarta.
Citilink's President Director Albert Burhan said, in a statement on Thursday evening: "Citilink is very serious about handling this matter. The pilot in question has been suspended until the ongoing investigation is completed."
The airline confirmed he had appeared "physically unfit" but the final results of a medical check will be issued in a week.
It has since emerged that the pilot and two of Citilink's executives, including the president, are resigning.
Burhan announced today that he and the airline's production director would resign over the impropriety. Citilink is a subsidiary of national flag carrier Garuda Indonesia.
"The pilot had committed serious violation of standard operation procedure that endangered passengers," Burhan said. "We apologise for the discomfort. I have to be responsible for that and therefore I and my production director resign."
The airline previously had dismissed reports that the 32-year-old pilot Tekad Purna was drunk, saying initial tests of drug and alcohol were negative.
Director General of Air Transportation Suprasetyo has asked Citilink to make sure the pilot underwent a medical check.
Purna is under investigation for possible drunkenness or drug use. Minister of Transportation Budi Karya has banned him from flying pending the outcome of the investigation. If proven, his license would be revoked.
In December last year, three crew members - a pilot and two flight attendants were arrested for allegedly consuming crystal methamphetamine, known locally as shabu-shabu, at a hotel.
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