Cseh was fastest with 1:57.20, while Phelps was fourth with 1:58.24 and Ryan Lochte second quickest.
Phelps, who became the most decorated Olympian of all time with last night's 19th medal, said: 'I didn't get much sleep last night, I didn't warm down at all.
'I guess we left the dining hall at 11.30 and got to the room at 12. I don't know when I fell asleep. This morning didn't feel too comfortable.'
Tyler Clary topped the 200m Backstroke heats ahead of defending champion Lochte, while Rebecca Soni started the defence of her 200m Breaststroke title as comfortably the fastest qualifier.
Tang Yi heads the women's 100m Freestyle and Australia were quickest into the women's 4 x 200m Freestyle Relay final.