Trump said the attacker was a "radical Islamic terrorist," using a term he has used previously to describe such attackers.
"A new radical Islamic terrorist has just attacked in Louvre Museum in Paris. Tourists were locked down. France on edge again. GET SMART US," Trump wrote on Twitter.
In a briefing earlier this week, a senior US administration official defended the temporary US travel ban on refugees and other travelers from seven predominantly Muslim countries by saying America was trying to avoid the security situation in France and other European countries.
"We don't want a situation where, 20 to 30 years from now, it's just like a given thing that on a fairly regular basis there is domestic terror strikes, stores are shut up or that airports have explosive devices planted, or people are mowed down in the street by cars and automobiles and things of that nature," the official added.
The attacker is in a serious condition, while one soldier received a "minor" head wound and has been taken to hospital, security forces said.
Two backpacks carried by the assailant were checked by bomb disposal specialists at the scene and were found not to contain explosives.
The incident sparked fresh jitters in a country still reeling from a string of terror attacks over the last two years and under a state of emergency since November 2015.
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