The driver received a facial injury on Monday night while on duty.
The diversions are affecting Metro and Ulsterbus services.
After consultations with the PSNI and Trade Unions, Translink announced their decision, adding that they will continue to monitor the situation in east Belfast and all other parts of the city taking appropriate action when required.
Catherine Mason, Group Chief Executive at Translink, said: "The safety of our passengers and employees is a priority and our highest concern.
"Last night in an attempted hijacking one of our drivers sustained facial injuries - our thoughts and concerns are with him and our other colleagues who have been impacted by this recent disorder. In light of this we have no option but to adjust our evening bus services to continue to operate safely.
"We would thank our colleagues driving buses who have continued to deliver services as far as they could in these difficult circumstances and worked hard to get passengers home. We have received many expressions of thanks and support."
Around 100 police officers have been hurt since the start of the flag dispute last month, while over 110 people have been arrested.
It began after Belfast councillors voted at the start of December to restrict the flying of the Union flag over City Hall to 18 designated days.