Police described him as Syrian, and German media reported that he arrived in Germany in December 2022, after leaving the war-torn country.
Bild reported that Special Task Force (SEK) officers stormed a refugee center that the suspect was associated with, detaining another person there.
Police also arrested a 15-year-old boy who is alleged to have known about the attack in advance.
The refugee center is located about 300m (984ft) from Fronhof-Solingen’s central market square where people were stabbed on Friday night – according to Bild.
Solingen – a city famous for its steel industry – has about 160,000 inhabitants. It lies about 25km (15 miles) east of Düsseldorf.
The city’s authorities asked people to leave the Fronhof area after the attack at about 22:00 local time (21:00 BST) on Friday.
The planned three-day celebrations of the city anniversary – for which about 75,000 people had been expected – were canceled after the attack.
Solingen Mayor Tim Kurzbach later said “all of us in Solingen are in shock, horror, and great sadness.
“It breaks my heart that an attack has happened in our city. I have tears in my eyes when I think of those we’ve lost.
“I pray for all those still fighting for their lives. Also my greatest sympathy for all those who had to experience this, these images must have been horrific.”
People have been bringing flowers and candles to the site of the attack which shocked the entire country.
Players from Germany’s top Bundesliga football league wore black armbands during Saturday’s matches.
The attack may fuel an already fraught debate about immigration and asylum in Germany.
It comes ahead of key regional elections in the country’s east next week, where the far right is eyeing gains.