Riot police and plainclothes officers jostled with union leaders and other demonstrators and threw some to the ground before detaining dozens of them near Istanbul's Taksim Square.
The governor's office said some labor unions were allowed to hold memorials to mark the annual holiday, while others who had "gathered illegally" in violation of the lockdown, and ignored calls to disperse, were detained.
Some 20 protestors were also detained in the western city of İzmir.
Turkey this week adopted a 17-day partial lockdown, including stay-home orders and the closure of schools and some businesses, to curb a wave of coronavirus infections.