Mzee Mohammed, 18, became unwell at Liverpool One and was pronounced dead in hospital on Wednesday night.
Friends and supporters walked from Liverpool Lime Street station towards the spot where he collapsed.
In a statement, his family said: "He was more to us than a son, brother and nephew, he was our friend."
They added they wanted the community to come together to support them in "a peaceful and quiet" event.
A post-mortem examination into Mr Mohammed's death was inconclusive and further tests are to be carried out.
His mother Karla said she wanted "a full transparent investigation" to take place.
The Independent Police Complaints Commission is already investigating, as it does with all deaths in custody.
The family of a man who died while in police custody, after being detained by security staff at a shopping centre, has led a vigil in his memory.