Karlberg shot a 7-under 64 at the Golf Club Milano, next to Monza's Formula One circuit.
Thunderstorms delayed play for several hours and a good chunk of the field did not complete their rounds, or even start.
Robert Karlsson of Sweden and Adrian Otaegui of Spain were tied two strokes back.
Italian amateur Federico Zucchetti was among several players at 4 under.
Karlberg rolled in an 18-footer for an eagle on the ninth, his final hole of the day.
''That's as good as it gets,'' Karlberg said. ''I kept my cool even though it was a longer day. Standing over the last shot on the ninth green, I just told myself, 'I'm so tired but it's just one more shot.' Pleased to execute as good as I did.''
Molinari is attempting to become the first Italian winner of the title since his maiden European Tour win a decade ago.
The first round will be completed on Friday.