The ICC found opener Roy had breached level one of its code of conduct, using an audible obscenity after a misfield during Pakistan's innings.
Archer was found guilty of dissent towards an umpire's decision following a wide delivery.
Both players have also had one demerit point added to their records.
Pakistan captain Sarfaraz Ahmed was fined 20 per cent of his fee, and his teammates 10 per cent, for a minor over-rate offence.
It was an occasionally fractious encounter, with the umpires warning Eoin Morgan about his side throwing the ball in on the bounce and later issuing the same reminder to Sarfaraz.
England batsman Jos Buttler appeared to take a look at the ball on his walk back to the pavilion after his knock of 103 came to an end.