The 30-year-old midfielder scored on his City debut against Birmingham City in the Carling Cup after three injury-ravaged years at rivals Manchester United.
"Everybody is delighted for Owen because it has been well documented the injury problems he has had over recent years," Marwood told BBC Radio Five Live. "He has worked hard to get back to the level of fitness at which he can compete in the Premier League.
"We are all hopeful he can stay healthy because he can make an enormous contribution not only to Manchester City, but potentially to the England national team."
Hargreaves will not feature in the Blues' Champions League tie against his former club Bayern Munich on Tuesday after he was left out of their European squad.