The row has hit Raila Odinga's relations with President Kibaki.
Kenya's government has launched an investigation into claims of illegal maize trading that have raised fears of a new rift in its fractious coalition.
Agriculture Minister William Ruto said post-election violence had helped cause shortages of the staple crop, rejecting claims of corruption in his ministry.
He spoke after Justice Minister Martha Karua blamed cartels in the agriculture ministry for the shortages.
More than a quarter of the population are said to lack food.
Kenya's government warned last week nearly 10 million people were at risk from food shortages and said it would declare a national emergency.
President Mwai Kibaki's administration said it was taking the justice minister's allegations very seriously, and that Kenya's Anti-Corruption Commission and other state agencies would now establish the truth.
"The findings will be made public and appropriate action taken," spokesman Alfred Mutua said in a statement.
Ms Karua is from the president's Party of National Unity, while Mr Ruto is an ally of Prime Minister Raila Odinga, who joined the government of national unity under a deal to end last year's bloodshed.
Officials in the agriculture ministry have been accused of creating a maize shortage by dealing with unscrupulous traders who sell maize outside the country, inflating the prices for Kenyan millers.
But Mr Ruto told the BBC's Network Africa programme the reasons for food being in short supply were soaring fertiliser costs due to the global financial crisis and last year's poll-related bloodshed.
At least 300,000 people were displaced in the disorder, many of them farmers who have been too frightened to return home and plant crops.
A 2006 drought in Kenya left thousands of people facing starvation
"I've already sent a notice prohibiting any sale of maize outside the country," said Mr Ruto.
"Martha Karua and those who are saying there is corruption leading to maize shortages are just playing politics.
"If she knows of any such deals she should inform the relevant authorities."
It is the latest public row to hit Kenya's coalition government.
Mr Odinga and his Orange Democratic Movement (ODM) party last week held crisis talks to assess their position in the coalition after claiming they were being sidelined by President Kibaki.
They complained they had not been consulted about important decisions on a controversial media law, electoral reform and new ambassadors.
Meanwhile there are reports that that low-priced government maize flour launched two months ago had still not reached rural areas where it is badly needed.
In Baringo District, hundreds of thousands of people have been stricken with hunger and some were surviving on wild roots, according to Kenya's Standard newspaper.