The suspect – confirmed to be a woman by a Monaco judicial source – has since been spotted in Germany, said the source.
The parcel bomb blast in the wealthy principality was believed to be an attack on a Ukrainian-born oligarch.
He was named in local news outlets as Vadym Iermolaiev, with Ukrainian media claiming he has previously been targeted with sanctions because of his ties to Russia.
Police opened an attempted murder investigation at the time but did not qualify it as a terrorism investigation, prosecutor Stephane Thibault said.
One of the three injured people is a woman who was in a life-threatening condition, he said earlier this week.
The other two are a man who was no longer in a life-threatening condition and a child whose life was not in danger, he added.
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The search for the suspect is continuing, and authorities have launched an arrest warrant.
They have also issued an Interpol red notice, which is a request for law enforcement to locate and provisionally arrest a suspect no matter where they are found.
