Raising the issue in the assembly on the first day of the monsoon session, senior Nationalist Congress Party leader and former Deputy Chief Minister Ajit Pawar asked: "How they could be inducted as ministers without being members of either house of the legislature".
While Vikhe-Patil recently quit the Congress and as legislator from Ahmednagar, Kshirsagar left the Shiv Sena and resigned as MLA from Beed.
Both joined the BJP and were sworn-in as ministers on Sunday by Governor C.V. Rao.
Justifying their induction, Chief Minister Devendra Fadnavis said that it was done in an absolutely Constitutional manner and there was nothing wrong in it.
"One is eligible to become a minister for six months without being a member of the House," he said.
While Vikhe-Patil has been allotted the crucial housing ministry, Kshirsagar has been entrusted with the employment guarantee & horticulture portfolios, even as the state will go to the polls after around four months.
When the treasury benches cited the example of former Chief Minister Narayan Rane, Pawar retorted that Rane had first resigned as a Shiv Sena legislator, contested and won elections on a Congress ticket, before joining the then Democratic Front government as a minister.
( With inputs from IANS )