Prosecutors and police said in a statement they had received "isolated indications that those arrested (Sunday) between the ages of 18 and 21 may have been involved in planning a violent crime in connection with this event".
The newspaper reports the men have suspected links to a Tunisian man who killed 12 people in the city in a December 2016 truck attack.
Police had put the men, aged 18 to 21, under surveillance and made a decision to use their powers of preventive arrest rather than risk an attack, Die Welt reported.
The German daily Die Welt first claimed that police foiled a plot to assault race spectators and players together with knives. Police have not released the names of the men who have been detained or any information about the charges they face.
In Berlin, police conducted raids before the race started, including a house that was searched after the Christmas market attack. It also wrote that in one of the searched apartments, dogs trained to find explosives barked when they were taken into the dwelling's basement.
Runners at the half marathon today.
Berlin's top security official, Andreas Geisel, had said that the city of 3.5 million people would need to review its precautions for the half marathon following the Muenster attack in which two people were killed.
The half-marathon was being guarded by some 630 police officers, German news agency dpa reported.
He said that, while the government would do its utmost to protect citizens, "absolute security is unfortunately not possible".
Anis Amri was shot dead in Milan days later after a Europe-wide manhunt.
A court last month sentenced a 26-year-old Palestinian asylum seeker to life in prison for killing one and wounding six others with a knife in a Hamburg supermarket out of a "jihadist" motive last July. No major Islamist attack has been carried out in the country since then.
The Berlin Half Marathon attracted 36,000 runners on Sunday morning, along with an unknown number of spectators.