Mandhana, who represented Brisbane Heat in the Women's Big Bash League, had hurt her knee during a match against Melbourne Renegades on January 15.
Meshram was originally left out for the World Cup qualifiers though she was part of the ODI squad in India's most recent series - against West Indies in November. She has played eight 50-over matches for her country having made her debut in June 2012.
India play a practice game against South Africa on February 5 before they start their World Cup qualifiers campaign against hosts Sri Lanka on February 7.
The tournament also includes Pakistan, Bangladesh, Zimbabwe, Ireland, Scotland, Thailand and Papua New Guinea. The top four teams go through to the World Cup, joining Australia, England, New Zealand and West Indies who automatically qualified through the ICC Women's Championship. World Cup 2017 will be held from 26 June to 23 July in England.