The arrest followed an outbreak of violence during Super Lig club Ankaragucu's home match against Rizespor on Monday evening.
Referee Halil Umut Meler, who was also kicked while lying on the pitch, said that Koca had also threatened him and his colleagues, state-owned Anadolu news agency reported.
"Faruk Koca punched me under my left eye; I fell to the ground. While I was on the ground, other people kicked me in the face and other parts of my body many times," he said.
"Koca said to me and my colleagues, 'I will finish you'. Addressing me, he said, 'I will kill you'."
The Turkish court which made the arrest ruling also remanded in custody two other suspects over the incident.
"This incident developed due to the wrong decisions and provocative behaviour of the referee. My aim was to react verbally to the referee and spit in his face," Koca told the court, according to Demiroren News Agency.
The Turkish Football Federation (TFF) said it had suspended all leagues after the "shameful" incident in Ankara.
Justice Minister Yilmaz Tunc said Koca and two others were formally arrested for "injuring a public official" after prosecutors took statements from them.
"The investigation is continuing meticulously," he said on social media platform X, adding judicial controls were imposed on three other suspects.
Koca entered the field and hit Meler when the final whistle blew after Rizespor scored a 97th minute equaliser in the 1-1 draw at Eryaman Stadium, footage showed.
The referee was lying in a hospital bed with a swollen face and a neck brace, footage provided by the ministry showed.
"The bleeding in Meler's left eye started to decrease" and there will be no permanent damage, said Mehmet Yorubulut, chief doctor of Acibadem hospital.
"The fracture there will gradually heal. There is no brain damage," he said, adding he will likely be discharged on Wednesday.
The club president Koca was twice elected to Turkey's parliament as part of President Tayyip Erdogan's ruling AK Party.
PITCH INVASION
After the match, footage showed Ankaragucu fans invaded the pitch and Meler was also kicked when he fell. He eventually made it to the dressing room with the help of the police.
The federation said Ankaragucu, its chairman, club officials and all those guilty of attacking the referee will be "punished in the strongest terms possible".
FIFA President Gianni Infantino said the events that took place after the match were "totally unacceptable and have no place in our sport or society".
"Without match officials there is no football," he added.
European football governing body UEFA also condemned the incident.
"We urge the authorities and the responsible disciplinary bodies to take decisive and necessary action against anyone involved in acts of abuse and violence against referees," UEFA said.
"Such unacceptable and distressing behaviour is detrimental to the efforts of national associations to recruit referees, which are essential for the running of the game."
Pierluigi Collina, chairman of FIFA's referees committee, described images of the incident as horrific.
"Neither the referee, nor the man, deserved to live the experience he lived yesterday in Ankara. He was doing his job when he was assaulted on the field of play at the end of a match he just officiated," Collina said.
"Even more horrific is to know that there are thousands of referees around the world who are verbally and physically abused at lower levels of the game across the world, without being reported by media."
Referees in Turkey are often criticised by club managers and presidents for their decisions but are rarely the target of violent attacks.
Ankaragucu are 11th in the standings on 18 points, three places below Rizespor on 22 points after 15 matches. It is unclear when Super Lig matches will resume.
