The suspect was also "unfavourably known" by police authorities in France and Germany, Castaner told reporters on Wednesday, adding that he was known for non-terror related offences.
French gendarmes had attempted to bring him in for questioning Tuesday morning before the attack but found he wasn't home, a spokesperson for France's National Police told CNN, without providing further details.
'People running, scared, crying kids'
Issam Fares, who sells chestnuts at the Strasbourg Christmas market, told AFP he heard several shots and thought they were fireworks "or they're attacking a store."
"I saw a lot of people running, scared, crying kids and all. Then I said, in my opinion it must be very, very serious, and then ... I saw people crying and the crowd leaving," he told AFP. "They said it was shooting right next door, so I ran away. I went to hide in a restaurant, not far from Gutenberg Street."
The injured were taken to a Strasbourg hospital.
French President Emmanuel Macron tweeted early Wednesday in solidarity with the French people. "Solidarity of the whole Nation for Strasbourg, our victims and their families," he said.
Terror attacks across Europe
The threat of terrorism has become a grim fact of life for parts of Europe, which has seen attacks on a Christmas market in the German capital Berlin in 2016, suicide bombings at Brussels Airport and a nearby Metro station that same year, and attacks on a busy downtown Barcelona avenue and a nearby Mediterranean beach resort last year, killing 13.
In the wake of the 2015 Paris attacks, French authorities launched a military operation called Opération Sentinelle -- in which 10,000 soldiers, police and gendarmes were deployed in Paris and its suburbs.
Strasbourg, a picturesque city of about 300,000 in France's Grand Est region on the border with Germany, has previously been at the centre of French counter terrorism operations. The market itself was targeted 18 years ago in a thwarted plot by al Qaeda-linked terrorists.
In 2016, French authorities arrested seven people in anti-terror raids in Strasbourg and Marseilles. In 2012, police killed one suspect and arrested 10 others in the city as part of coordinated counter-terrorism operations.
Schools closed, Christmas events canceled
Following Tuesday's attack, the European Parliament in Strasbourg was placed on lock-down as the search for the gunman continued. Tweeting from inside, European Parliament President Antonio Tajani said that Parliament will "not be intimidated by terrorist or criminal attacks." He expressed "sorrow" for the victims, adding that Parliament will "continue to work and react strengthened by freedom and democracy against terrorist violence."
Containment measures were lifted hours later with police warning everyone to remain vigilant and follow safety instructions.
British Prime Minister Theresa May wrote on Twitter that she was "shocked and saddened" by the "terrible" attack in Strasbourg. "My thoughts are with all of those affected and with the French people," May tweeted.
The Christmas market will be closed Wednesday and flags will be at half-staff, Strasbourg Mayor Roland Ries said on his Twitter account. All shows scheduled to be performed at the city's cultural institutions will also be cancelled on Wednesday, the mayor said.
Strasbourg's local department of education said all the city's kindergartens and elementary schools will also be closed on Wednesday.