"Horses are not bred for human consumption," Meehan said in a statement. "Horses are routinely treated with drugs over the course of their lifetimes that are toxic to humans if ingested."
The bill lists 12 potentially dangerous chemicals that could move into the food chain if horses are slaughtered for consumption.
The drugs' side effects in humans range from skin lesions to tremors to liver damage to heightened susceptibility to infection, studies show.
Meehan's bill had 20 cosponsors Wednesday. A similar measure in the Senate was introduced by Mary Landrieu (D-La.).
Lawmakers argued that horses sold for food also experience "brutal and inhumane" conditions.
The last ban on slaughtering horses for consumption lapsed in 2011.