Dahir A Adan is a Kenyan-born ethnic Somali who had been in the US for 15 years, his father told the Minneapolis Star Tribune.
He said he had "no suspicion" that his son was involved in extremist activity.
Nine people were injured, but no one died, in Saturday evening's attack at the Crossroads Center mall.
The Islamic State group claimed responsibility. Rasd, a news agency linked to the group, claimed on Sunday the Minnesota attacker was a "soldier of the Islamic State".
The attacker, who was dressed in a security uniform and carrying what appeared to be a kitchen knife, reportedly made at least one reference to Allah and asked a victim if he or she was Muslim before attacking, said police.
Adan had been working as a security guard for the mall's Electrolux Home Products store, according a company spokeswoman.
He was employed by security firm Securitas, she added.
The victims included seven men, one woman and a teenage girl at the shopping centre in St Cloud, 70 miles (110km) out of Minneapolis.
The knifeman was shot and killed by an off-duty police officer.
Authorities have not identified the attacker.
But Ahmed Adan said police had told him at around 9pm on Saturday that his son died at the mall.
Investigators searched the family's apartment, seizing photos and other materials, said Mr Adan.
Police had three previous encounters with the attacker, mostly for minor traffic violations, Police Chief Blair Anderson said.
Adan was a student at St Cloud State University, but had not been enrolled since spring.
Minnesota has the nation's largest Somali community, according to US census figures.
Jaylani Hussein, of the Council on American-Islamic Relations, expressed concern for the state's community of 40,000 or more Somali-Americans.
"We are definitely concerned about the potential for backlash in the community, both in the immediate run and the longer term," he said on Sunday.
The community has been a target in recent years for terrorism recruiters.
More than 20 young men have left the state in recent years to join al-Shabab in Somalia.
About a dozen others have left in recent years to join militants in Syria.
Nine Minnesota men currently await sentencing on terror charges for plotting to join the Islamic State group.
A knifeman who stabbed nine people at a Minnesota shopping centre at the weekend has been identified by his father as a 22-year-old student.