In conjunction with the English Football League and Women's Super League, the Premier League announced Friday it was suspending play until April 4 due to fears over the coronavirus.
Writing in The Sun newspaper, Brady argued it's unlikely teams will have enough time to complete the rest of the campaign.
Premier League clubs are expected to discuss the next steps in an emergency meeting Thursday.
"So what if the league cannot be finished?" Brady wrote. "As games in both the PL and in the EFL are affected, the only fair and reasonable thing to do is declare the whole season null and void.
"Who knows who would have gone down or come up if the games have not actually been played in full?"
Brady's proposal would essentially rob Liverpool of a first Premier League title in club history. The Reds are just six points away from clinching the trophy in what has been a runaway season.
"The PL hopes that an interlude of three weeks from today will enable it to restart but that may well be dreamland," Brady added.
"Perhaps scrubbing the European Championship could provide more time to complete the season into the summer but that is also a giant 'if.'"
Brighton & Hove Albion chief executive Paul Barber said it would be "incredibly unjust" if Liverpool were denied the title and if other teams were relegated based on their current standing.
"I think everybody in the game appreciates what a fantastic season they've had and what a wonderful team that they are. ... But equally, it would be unjust for teams to be relegated when there are still eight, nine, 10 games to play in the Premier League ... and equally unjust for Leeds and West Brom not to be promoted," Barber told BBC Sport.
West Ham are currently in 16th place with 27 points, just outside the relegation zone on goal difference.