The left-hander underwent scans in Sydney on Tuesday which revealed a low-grade tear to his right hamstring.
Marsh suffered the injury while batting during Australia's 51-run win in Brisbane on Sunday, which sealed the series 4-1.
Callum Ferguson has been called up as cover for Marsh and will join the team ahead of Wednesday's sixth one-dayer in Sydney.
"Scans have confirmed Shaun has a low grade right hamstring injury," Australia team physiotherapist Alex Kountouris said.
"He will return to Perth today and will be reviewed again later this week when the Australian team arrives for the final match of the Commonwealth Bank Series.
"He will be unavailable for the two remaining ODI games against England and his return to cricket will be determined by his progress over the next week."
With the injury not deemed serious Marsh's World Cup hopes have been boosted.
The Western Australian has been touted as the likely replacement for Mike Hussey whose fitness is in doubt for the tournament after he required hamstring surgery earlier this month.
Ferguson, who averages 46.07 in 26 one-day internationals, will therefore get his chance to press his claims.
"Callum has an excellent record in one-day internationals for Australia and is in good form this season," chief Australia selector Andrew Hilditch said.
"We are sure Callum will seize the opportunity that comes following the unfortunate hamstring injury suffered by Shaun Marsh."