Scottish Liberal Democrat leader Alex Cole-Hamilton has written to the commission, calling on it to carry out a statutory inquiry to examine if the proposals breach equality laws.
It comes days before the Scottish Government’s controversial vaccine certification scheme is due to come into effect.
From Friday October 1 people will have to prove they have been double vaccinated before they can enter nightclubs or attend some other large events.
The Night Time Industries Association (NTIA) confirmed last week it planned to mount a legal challenge to the controversial scheme, which Labour, the Tories and the Liberal Democrats all voted against in Holyrood.
Judith Robertson, chairwoman of the SHRC, told MSPs the case for the passports had not been publicly made.
Mr Cole-Hamilton said: “I have a real concern that these illiberal Covid ID cards will lead to ethnic minority Scots, young people and those from the most deprived areas being systematically excluded from public events and spaces.
“The SNP/Green Government are rushing this through and appear to have no intention to share evidence to back their plans up.
“I believe this is precisely the kind of situation where the commission, set up by Labour and the Lib Dems, should kick in.
“Their power to instruct an inquiry may be the only way to get behind the curtain on this.”
The Scottish Lib Dem leader branded the scheme a “hugely significant policy decision” from First Minister Nicola Sturgeon, which he insisted “goes against the very basic freedoms at the heart of our society”.
Mr Cole-Hamilton said: “The SHRC previously warned that the Scottish Government would need to demonstrate Covid ID cards were necessary, proportionate and effective.
“In my view, none of these tests have been met.
“Ministers should be taking all the resources devoted to this cruel policy and using them in the ways we know tackle Covid-19 – testing, tracing and vaccinating.”
He spoke out after Ms Robertson told MSPs on Holyrood’s Covid-19 Recovery Committee “that case has not been made at the moment” for the scheme “or if it has it’s not in the public domain”.
She said: “That is one of the key aspects in relation to those human rights considerations: that the evidence upon which decisions are being made be placed into the public domain so that not only the basis on which decisions are being made is clear but that can be interrogated by a wider element of the population.
“There isn’t a clarity around what evidence has been used to base the decisions on.”