Marsh hospitalised with Covid as IPL's Delhi suffer virus outbreak
The Delhi Capitals medical team is closely monitoring the condition of Marsh, who played his first match of the Indian Premier League season on Saturday.
Other positive cases, including in the support staff, are all "asymptomatic", according to the statement.
All remaining members of the bio-bubble are currently in isolation and will be tested regularly, with Delhi scheduled to play their next match on Wednesday against Punjab Kings in Pune.
Delhi physio Patrick Farhart tested positive for the virus last week but no other cases were reported as Delhi went on to play their game against Royal Challengers Bangalore at the weekend.
The 15th edition of the Twenty20 tournament is underway, with league matches being played across four venues in Mumbai and Pune with 50 percent capacity crowds allowed inside stadiums.
India has recorded a slight increase in the number of Covid cases in recent weeks but is nowhere near the peak seen between March and May last year.
At least 4,000 people were dying every day at the height of the pandemic in 2021, according to official figures.
The health ministry on Monday reported over 2,100 new cases in the last 24 hours.
The IPL began in India in April last year but had to be suspended at the halfway point a month later as Covid infections surged across the country.
It eventually resumed in September in the United Arab Emirates, which also hosted the league in 2020 due to the pandemic.