Senate President Scott Ryan says state and territory COVID-19 quarantine requirements are undermining parliamentary democracy and setting a dangerous precedent.
Labor has also accused Prime Minister Scott Morrison of "sidelining" a cross-party working group set up to find ways the parliament could continue to meet during the pandemic.
Parliament resumed sittings for the first time in more than two months on Monday, despite many MPs and senators being unable to attend in person due to coronavirus restrictions.
MPs from Victoria were forced by the ACT government to quarantine at home or in Canberra for two weeks before attending parliament, while Queensland, Tasmania and Western Australia have revoked quarantine exemptions for returning politicians.
Senator Ryan said these "controls" on MP movements from the executive branches of government challenged important democratic principles, such as the Senate's ability to determine its own sitting schedule.
"The right of those elected to attend and participate in parliament is an ancient one," Senator Ryan said.
"For good reason the ability of others, including the executive to restrict this has always been limited. The powers and immunities that enable and secure the work of the two Commonwealth houses belong to the houses themselves by constitutional design, a design that ensures the Senate in particular can undertake its functions with an appropriate degree of independence.
"The ability to scrutinise the executive ... is unarguably even more critical in times of crisis due to the extraordinary powers being delegated, granted and exercised by officials and the executive.
"In the current pandemic an important principle is at stake, notably the ability of the executive or its officers no matter the jurisdiction to control attendance at parliament or constrain the work of members of parliament when it is directly related to parliamentary proceedings."
Senator Ryan said of greater concern was the discretion some governments, including the ACT, were using to determine which senators and MPs could attend parliament.
"In the case of the ACT permits were granted to ministers to attend events prior to the sitting of parliament but the attendance of senators and members to a session of parliament on the same basis was denied and claimed to be prohibited," Senator Ryan said.
"This claimed discretion is particularly problematic on the grounds of differential treatment of members of the executive in the first instance and a lack of transparency around the equality of treatment of senators in the second.
"The explanation that the medical risk posed by the entry of a single minister is lower and therefore allowable as opposed to a group attending an actual session of parliament is a circular one with a dangerous consequence in that it establishes a preference for members of the executive attending events not directly related to parliamentary proceedings but then effectively claims the power to control of prohibit parliamentarians attendance at actual parliamentary proceedings."
Senator Ryan said "unilateral action" from executive governments - whether state, territory or Commonwealth - that impeded the performance of the parliament "are problematic from a constitutional perspective".
"The national parliament is a critical part of government which we are relying on through various agencies and experts to manage our response and care for the health and interests of our fellow Australians," Senator Ryan said.
"In my view, simple acquiescence to these new assertions of control by officials of the executive of Commonwealth, state or territories including somewhat extraordinarily the territory established as the seat of government and that we are constitutionally required to assemble in, poses a risk in that we cannot envisage how it may be used or potentially even misused at a future time in circumstances we cannot imagine."
Labor senator Penny Wong also said ceding "untrammelled power" to executive governments was risky.
"Put simply Mr President, parliamentary democracy needs a parliament. It's not an optional extra," Senator Wong said.
However she accused Mr Morrison of sidelining a working group set up to determine how parliament could meet safely.
"As you might recall, the presiding officers government and opposition managers of business chief medical officers were meeting to ensure this was done collaboratively," Senator Wong said.
"Regrettably the prime minister unilaterally commissioned advice and sidelined the working group."
Labor urged the presiding officers to commission independent medical advice about how the parliament could continue its work during the pandemic.