Ottawa is asking the court for guidance on what it would take to reform the upper chamber and whether it can abolish the body without provincial consultation.
Manitoba Attorney General Andrew Swan says the upper chamber is basically flawed and should be abolished, but he cautions that the federal government can't go it alone.
The province's submission argues that Parliament does not have the constitutional authority to enact significant unilateral changes to the structure of the Senate or to the selection of its members.
Swan says such changes require consultation and agreement with the provinces.
"Here in Manitoba, the provincial senate was abolished in 1876," Swan in a statement.
"In our view, the Senate is fundamentally flawed and it's time to abolish it. I urge the federal government to engage the provinces in consultation with the ultimate goal of finding consensus to abolish the upper chamber."
If the Senate is not abolished, Swan said, its members should be elected.
In 2009, Manitoba's all-party committee on Senate reform recommended the federal government administer and pay for elections of senators in the provinces and that these votes be held alongside federal elections.
A private member's resolution calling for the abolition of the Senate has been tabled in the provincial legislature.