Mr Modi has saved money on the central government's social and subsidy expenditure and channelled it into an infrastructure stimulus that he hopes will trigger a spurt in economic growth.
"This may result in a situation where the focus is lost on critical programmes related to malnutrition of children... nutrition for pregnant and lactating mothers," Maneka Gandhi wrote in an April 27 letter to Finance Minister Arun Jaitley.
"I am afraid to point out that political fallout of such a situation can be grave," she wrote, according to news agency Reuters. Ms Gandhi is Minister for Women and Child Development.
The government says lower welfare spending will be compensated for by giving state governments a larger allocation of tax revenues to spend as they choose. But some Chief Ministers, including Nitish Kumar, have alleged that they are being shortchanged. (NDTV.com Exclusive: PM's Cooperative Federalism is Mere Rhetoric)
In its first full-year budget, approved by Parliament on May 7, Mr Modi's government halved funding for a scheme that gives millions of poor children free food and drastically cut allocations to make clean water available in rural areas.
On the other hand, funding for roads and bridges more than doubled and is now higher than the sum allocated to education.
Four of 10 stunted children in the world are Indian, more than sub-Saharan Africa. About 1.5 million children die each year before the age of five.
Mr Modi's first year in office has seen a string of successes, including forging closer ties with major trading powers, boosting foreign investment and cutting red tape.
But he has been facing a united opposition over his new land reforms, which have been described as "anti-farmer" by critics at a time when farmers are combatting bad rains and low crop prices.
"Increasing signs of rural distress in India make Modi's cuts politically risky," said Milan Vaishnav of the Carnegie Endowment for International Peace.
At the same time as taking away central funding, Mr Modi has increased the share of taxes given to states to 42 percent from 32 percent, money that, if well spent, can cover the shortfall from the spending cuts.
States will this year receive about $28 billion (nearly Rs 1,78,000 crore) more taxes, while the cuts reduce support to central programmes run by states by about $18 billion (nearly Rs 1,14,000 crore, according to the Centre for Budget and Governance Accountability.
While that's an overall gain of $10 billion, poorer states who rely more on central support say they face net losses.
Naveen Patnaik, Chief Minister of the impoverished state of Odisha, lodged his protest in an April 29 letter to Mr Modi, saying the new policies put a burden of $335 million (nearly Rs 2,100 crore) on Odisha, a cut that is "beyond its means".
"The loss... is not going to be set off by the 10 (percentage point) increase in devolution," he wrote. "This will have an adverse impact on the social economic development of some of the most vulnerable and backward regions of the country," he said in the letter, according to Reuters.
Officials from the Health Ministry have told a parliamentary panel that the budget will have a "major impact" on plans to provide free medicine and strengthen clinics.
"Past experience shows that if spending is left to the states... (health) will take a back seat," the panel said in its report.
Health Minister JP Nadda has publicly denied a shortfall in the health budget.