The group - Wales Assembly Against Racism - has said the demonstration will also carry the torch for asylum seekers in Liverpool and Rochester prisons.
This latest protest follows a week-long hunger strike in Cardiff by around 30 detainees.
The men said they were angry at being detained in jail while their applications to remain in the UK were being determined.
They claimed immigration officials deceived them by not informing them they were going to be housed in the jail.
The prison service denied that the asylum seekers were on a hunger strike claiming instead they were on "food refusal".
The men have been kept at the prison for about four months under a Home Office policy announced earlier this year to hold them while specialist detention centres are built.
The decision to detain the asylum seekers in jail has been widely criticised by members of the Welsh Assembly.
Jenny Randerson, Liberal Democrat AM for Cardiff Central said: "From the first, I have expressed total opposition to the UK Government's policy of holding asylum seekers in prison.
"In March I visited the prison and spoke to asylum seekers and prison officers and I saw the conditions there.
"The original assurances from the UK Government that only asylum seekers who had been rejected were to be held in prison were clearly untrue.
Locked in
"Many there were awaiting the outcome of their appeal. Although prison staff were doing their best, it was obvious that individuals were locked in for long periods of time."
Meanwhile a 26-year-old man is expected to appear in court on Monday in connection with the death of a Kurdish asylum seeker in Glasgow.
The stabbing of 22-year-old Firsat Dag two weeks ago sparked racial tension in the Sighthill area of the city.
The man detained was arrested at the weekend - along with another man - over an assault on a German tourist shortly after the death of the asylum seeker.