Anastasiia Berezovska, a 39-year-old woman from Ukraine, has been named as the suspect in a red notice posted on its website seeking her arrest.
The suspect has since been spotted in Germany, a source told the Reuters news agency.
A Monaco prosecutor said she was disguised as a man.
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.
Three people were injured, including 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.
