Toussaint, 77, had been touring in Madrid, Clarence Toussaint said in the statement.
Artists in nearly every major genre recorded Toussaint's songs or collaborated with him, including the Rolling Stones, the Yardbirds, Herb Alpert, Glenn Campbell, Robert Palmer and Alison Kraus and Elvis Costello.
They included the widely recorded "Fortune Teller," Campbell's chart-topping crossover version of "Southern Nights" and Leo Dorsey's 1966 cover of "Workin' in a Coal Mine."
His music, often by way of his house band The Meters, was also widely sampled by hip-hop artists such as Amerie, Public Enemy and N.W.A.