Kompany picked up a calf injury during the recent international break, but still played the full 90 minutes of Belgium's 9-0 victory over Gibraltar in World Cup qualifying.
The Mirror reports that Guardiola was furious with the centre-back for choosing his country over his club, having missed out on Saturday's 5-0 thrashing of 10-man Liverpool as a result of the injury.
Kompany could face another spell on the sidelines having endured a string of other injuries in recent seasons, and Guardiola is unhappy that the 31-year-old failed to recognise the issue and ask to be taken off against the international minnows.
City did not sign any new centre-backs during the summer transfer window, with a late bid for Jonny Evans falling through.
John Stones, Nicolas Otamendi and Eliaquim Mangala are Guardiola's other recognised central defenders in the squad, but the Spaniard could look to strengthen further in January following Kompany's latest setback.