The 22-year-old Olympic silver medallist pipped Switzerland's Noe Ponti in second place with Poland's Jakub Majerski in third.
Milak was in line to beat his own continental record of 49.68sec at the halfway stage before slowing down in the final 50m. Elsewhere, France's Analia Pigree claimed the women's 50m backstroke in 27.27sec, almost 0.30sec slower than the world record with Italy's Silvia Scalia in second and the Netherlands' Maaike de Waard taking bronze.
Romanian David Popovici claimed a place in the men's 200m freestyle final after breaking the world record in the 100m on Saturday.
Popovici, 17, finished in 1min 44.91 sec and will compete for another gold in Monday's late session but Milak will be missing from the race after having to settle for fourth place in his heat.