Construction, Forestry, Mining and Energy Union Western Australian assistant secretary Joe McDonald said the ban was "absolutely wrong".
"She still wants them to build her $70 million mansion, but she's telling them what they're going to eat . . . it's wrong," he said.
"I respect everybody's right to practice their religion, but I totally disagree with anyone forcing it on others.
"That has caused more wars and destruction throughout the world than anything else I know of.
"If people are working on the job and they want to have a ham sandwich or a bacon and egg sandwich, they should have one."
Mr Oswal, who is in New York this week helping Mrs Oswal prepare for the launch of her vegetarian fast-food chain, Otarian, defended the meat ban, saying "This is our home".
Mrs Oswal has previously accused the meat industry of "raping the earth".
"Meat eating is creating bad karma and you are also creating a vicious cycle," she said.
"It's destroying us environmentally, economically and socially. I'm putting my money where my mouth is. I've always been a vegetarian so I have always felt strongly about it.
"First, because of religious reasons, but then later because I realized the greater good associated with it."
The family does not eat meat out of Hindu tradition - although Radhika has previously said that the family is also keen to promote vegetarian diets as a sustainable option.
Below is a view of the construction site.
The riverfront mansion being built over eight blocks will feature seven bedrooms, 11 bathrooms, a fitness centre, beauty salon, dance area, meditation room, telescope room, waterways, extensive gardens, parking for 17 cars and a swimming pool 10 times the size of an average backyard.
But beneath the Oswals' ostentation lies a tale involving allegations of some unpaid bills, claims of broken promises and eccentric behaviour.
The Oswal's property, in Perth's top suburb Peppermint Grove, and is expected to be worth about $70 million when complete.
It is set to be the biggest home in the country on the most expensive block, which is alone worth $22.7 million.
