The top four tiers of English football have been suspended until 3 April at the earliest, with delays to the season expected to continue beyond that, and Brady said time constraints made completing the season an unrealistic prospect.
Writing in The Sun newspaper, Brady described the challenges clubs face in keeping players fit and healthy while the virus continues to spread around the world.
She said: "The issue is that medical advice is that for every day a player is in isolation he needs a day to recover his fitness.
"This on top of the issue that COVID-19 is so highly contagious the thought that everyone will be in and out of isolation and fit to play on 4 April seems so unlikely.
"So what if the league cannot be finished? 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."
Brady's comments come with West Ham languishing in 16th place in the Premier League table, level on points with relegation-threatened Watford in 17th and Bournemouth in 18th.
She admitted wiping this season from the record would infuriate the likes of Liverpool, which is poised to win its first league title since 1989-1990, but said people's safety must be put first.
"Who knows who would have gone down or come up if the games have not actually been played in full?" she said.
"A huge blow to Liverpool, [which] might be robbed of [its] first title in 30 years.
"This will be discussed between the PL and the clubs next week at an emergency meeting.
"There are, of course, financial implications, wages and transfer debts must be paid and there is lost broadcast revenue, lost match day income but this pales into insignificance as the health and well-being of everyone must come first."