Yes, it was, at least in the size of the prison population, and perhaps it was the largest in square footage, too. The former McDowell Medical College (which the Federals called Gratiot Street Prison) was a rather large institution. Late in the war the Union military also kept a number of some of the most dangerous war prisoners at the Missouri State Penitentiary at Jefferson City, but I don't know its size and only a few score war prisoners were kept there. Nearly all of the other military prisons across Missouri were either makeshift affairs using existing buildings to hold POWs for limited periods of time or were civil jails.
The Alton Military Prison (formerly a condemned state penitentiary) across the Mississippi River at Alton, IL housed a much larger number of prisoners, but you asked about Missouri.