The director of Positive Action in Housing (PAIH), Robina Qureshi, called for the commission's Scottish office to challenge the rule in the Court of Session and warned that campaign groups are likely to protest over the "discriminatory and unjust" policy.
Under strict criteria for volunteering for the Games, all applicants must be permitted to work in the UK, a regulation which rules out Glasgow's large population of asylum seekers, many from Commonwealth countries such as Pakistan, Nigeria and Sri Lanka.
Qureshi said: "The organising committee is supposed to ensure the Games celebrate diversity and inclusion, but the criteria they have set for volunteering breaches that.
"We think the EHRC should speak out on this important issue of diversity and launch a legal challenge in the Court of Session."
She added: "If they don't open their eyes and change that policy, the Games will be tainted, and we anticipate protests by refugee and human-rights groups."
Under current UK Border Agency (UKBA) rules, asylum seekers can volunteer in the UK but cannot take up paid work.
However, Glasgow 2014 organisers claim the criteria for volunteers was set after consultation with the Home Office, UKBA and the police.
Gary Christie of the Scottish Refugee Council (SRC) said: "The blanket ban has disappointed many refugees and asylum seekers.
"It would seem the organising committee have fallen at the first hurdle in ensuring the accessibility and diversity of the Games for everyone in Scotland.
A spokesman for Glasgow 2014 said they are "committed to delivering an accessible, diverse and inclusive Games".
He added: "We understand that most refugees and individuals with humanitarian protection status, and a small number of asylum seekers, will be able to meet the criteria.
"There may, however, be some who will not meet the criteria, or will not be able to provide the necessary documents. This will typically include those who have made recent claims for asylum.
"In these circumstances, we cannot anticipate whether individual cases will have been considered and concluded by Games time and therefore whether those individuals would be able to take up volunteer roles even if offered."
The spokesman added that the committee will look at other ways of ensuring refugees can get involved in the Games.
A spokeswoman for the EHRC was unable to comment.
ASYLUM seekers in Glasgow are disappointed at their exclusion from the Games.
Tabraiz Burki, 20, originally from Pakistan, said he was surprised to find out he was unable to volunteer as he has already carried out charity work in Scotland.
Burki, who has been in the UK for three years, said: "I really wanted to volunteer. I thought it would be a nice thing to do. I was really keen to get involved and contribute something. I'm really disappointed that I can't, as it would have been a great experience.
"Life as an asylum seeker is very monotonous and this would have allowed me to do something worthwhile. I won't be getting paid or anything so I don't see the problem."