The attacker left a parcel in front of a building in Monaco and set off the bomb with a remote control when the three victims arrived there, Monaco deputy prosecutor Morgan Raymond told reporters.
The suspect then left on foot to nearby France and fled with a car that had been rented in Germany, driving back to Germany via several European countries, including Italy.
Officials had said earlier this week that the suspect, whom they described at the time as male, was seen on CCTV wearing a dark bucket hat and top.
The sophistication of the attack has led investigators to consider it likely that the suspect did not act alone, Raymond said. Two people were arrested in Monaco earlier this week but have been released, he added.
The suspect was later spotted in Frankfurt, a judicial source in Monaco said.