Snyders's father ran a wine tavern in Antwerp that was allegedly once frequented by the painter Frans Floris, who is said to have squandered his fortune there. Whether the story is true or not, the son grew up around artists and became one of the first European painters to specialise entirely in animals.

He was born in Antwerp in 1579 and studied under Pieter Brueghel the Younger, though his painting style owed more to Brueghel's brother Jan ("Velvet Brueghel"), whose talent for rendering textures left a permanent mark. He may also have trained under Hendrik van Balen, who later taught Anthony van Dyck. A trip to Italy in 1608 to 1609 took him to Rome and Milan, where Cardinal Federico Borromeo became his patron.

Back in Antwerp, Snyders began collaborating with Peter Paul Rubens, a partnership that lasted from the 1610s until Rubens's death in 1640. Their brushwork was so close that contemporaries struggled to distinguish their contributions in shared canvases. Snyders painted roughly sixty hunting scenes and animal pieces after Rubens's designs, and added animal and still-life passages to Rubens's figure compositions. After Rubens died, Snyders served as one of the appraisers of his estate.

In 1611 he married Margaretha de Vos, sister of the painters Cornelis and Paul de Vos. He became dean of the Guild of Saint Luke in 1628 and bought a house on the fashionable Keizerstraat. His market scenes, hunt paintings and kitchen still lifes were compositions of Baroque excess: heaped game, overflowing fruit, dogs lunging at boar and deer. He died childless in 1657, at seventy-seven, leaving his fortune to his sister, a beguine.