Delph, who signed from Aston Villa after making a U-turn over his switch to City last week, lasted less than 20 minutes after a tussle with Luka Modric resulted in his early exit from the International Champions Cup game in Melbourne.
City will now face an anxious wait to determine the severity of the injury to their £8 million (€11.2m) signing, with their opening Barclays Premier League match against West Brom just over two weeks away.
“Unfortunately, it looks like Fabian has a problem with his hamstring — we thought it would be useful for him to play 45 minutes but he got the injury so it’s not the best news,” Pellegrini said.
“We will have a more clear diagnostic from the doctor tomorrow.”
The City boss was not too concerned following the heavy defeat by Real at the MCG after fielding an under-strength side.
Eliaquim Mangala did not feature after falling ill ahead of kick-off while Martin Demichelis, Sergio Aguero, Fernandinho, Pablo Zabaleta, Wilfried Bony and Vincent Kompany were also absent from the side.
It meant Jason Denayer partnered 16-year old Cameron Humphreys in defence against a formidable frontline of Cristiano Ronaldo, Isco, Gareth Bale and Karim Benzema.
“We knew before the game that it was difficult to play against a team with such good attackers without Mangala, Kompany and Demichelis,” Pellegrini said.
“You must also add the other players who are not here: Bony, Aguero, Fernandinho and Zabaleta.
“Especially defending, we knew it would be a difficult game. Mangala was sick this morning so he could not play and Kompany is becoming a father again so is not here.
“I’m not concerned as we had a lot of missing players and then a lot of players have also arrived late, so they’ve worked just five days. For them, they’re just starting work — it’s important in pre-season to work hard and good to play important teams but you can’t be worried about winning at this point.”