A nine-year-old child was among those killed when a car sped through the crowd at the busy festive market on Friday evening.
The suspect, a 50-year-old man from Saudi Arabia, was arrested at the scene and taken into custody.
Chancellor Olaf Scholz has labelled the incident a "terrible, insane act". (AP PHOTO)
Relatives of the victims, emergency responders and invited guests including German President Frank-Walter Steinmeier and Chancellor Olaf Scholz attended a private memorial service in the city's cathedral on Saturday evening.
"The Christmas market as a place of peace has been destroyed," Bishop Friedrich Kramer said.
Visiting the scene of the attack earlier on Saturday, Scholz called the incident a "terrible, insane act".
"There is no place more peaceful and joyful than a Christmas market," Scholz said.
"It is a horrific act to harm and kill so many people with such brutality in such a place."
Some 1000 people gathered outside the cathedral to watch the commemoration on a large screen. (AP PHOTO)
The chancellor also called for social cohesion, saying it was important to him "that we as a country stay together, that we stick together, and that we hook under each other, that hatred does not determine our togetherness".
During the memorial service, some 1000 people gathered outside the cathedral to watch the commemoration on a large screen, lay flowers and light candles.
The bells of the church rang exactly 24 hours after the attack, which took place shortly after 7pm on Friday.
Around 1000 people also gathered in a central square in the city, with some chanting far-right slogans and carrying flags showing the logo of the far-right, ultranationalist Homeland party, formerly called the National Democratic Party of Germany (NPD).
Right-wing groups have marched in the city of Magdeburg in response to the attack. (AP PHOTO)
Magdeburg is a city of some 237,000 people in the state of Saxony-Anhalt, some 150km west of Berlin.
Police in other German cities are now on high alert, with a spokesperson saying there would be an increased police presence at Christmas markets in Berlin.
The suspect, who has been identified as Taleb A according to German privacy laws, is being investigated on five counts of murder and 200 counts of attempted murder with grievous bodily harm, according to the head of the local public prosecutor's office, Horst Walter Nopens.
According to the current state of the investigations, the suspect was a lone perpetrator, police said.
The director of the Magdeburg police department, Tom-Oliver Langhans, said the suspect used an escape and rescue route to reach the Christmas market, with the whole incident lasting about three minutes.
The emergency route was not protected by barriers and the route had been designed to allow rescue services to access the market square in the event of an emergency, said city official Ronni Krug.
Taleb A is a 50-year-old doctor from Saudi Arabia, known as an Islam-critical activist. He has made erratic accusations on social media and in interviews, claiming German authorities are not doing enough to combat Islamism.
Previously an advocate for Saudi women fleeing their country, he later advised against seeking asylum in Germany, writing on his website in English and Arabic: "My advice: don't ask for asylum in Germany."
The motive for the crime is still unclear, but the suspect may have been unhappy with the treatment of Saudi refugees in Germany, prosecutors have said.
Taleb A arrived in Germany in 2006 and applied for asylum in February 2016 and was granted political refugee status in July of that year.
According to a spokeswoman for health company Salus, the suspect worked as a specialist in psychiatry in the forensic psychiatric ward in Bernburg, a town south of Magdeburg.
Saudi Arabian security sources said they had warned Germany about the suspected attacker.
Riyadh had requested the extradition of the suspect, but Germany had not responded, they said.
