Madonna - who has adopted two Malawian-born children - recently visited 10 primary schools funded by her charity.
The government accused the star of exaggerating her contribution to the country and demanding VIP treatment.
Madonna's manager accused Malawi's government of having a "grudge" against the singer's charity, Raising Malawi.
In a statement to the BBC, Trevor Neilson also accused the government of financial mismanagement of school project funds, and of "harassing organisations that Raising Malawi has donated to".
Madonna was said to have been angered that she and her entourage were stripped of their VIP status on their way out of the country, the UK's Daily Telegraph reported.
They had to line up with other passengers at the airport and were frisked by security officials, the report said.
The change in status was said to be the result of a public spat about her charitable work in Malawi.
End Quote Malawi government statementAmong the many things that Madonna needs to learn as a matter of urgency is the decency of telling the truth”
A harshly-worded statement issued by the office of President Joyce Banda on Wednesday accused Madonna of wanting Malawi "to be forever chained to the obligation of gratitude".
"Granted, Madonna is a famed international musician. But that does not impose an injunction of obligation on any government under whose territory Madonna finds herself, including Malawi, to give her state treatment. Such treatment, even if she deserved it, is discretionary not obligatory,'' said the statement.
It accused her of being "a musician who desperately thinks she must generate recognition by bullying state officials instead of playing decent music on the stage".
It added: "Among the many things that Madonna needs to learn as a matter of urgency is the decency of telling the truth.
"For her to tell the whole world that she is building schools in Malawi when she has actually only contributed to the construction of classrooms is not compatible with manners of someone who thinks she deserves to be revered with state grandeur."
Madonna's manager Trevor Neilson said buildOn, the non-profit group that partnered with Raising Malawi to construct the schools, was "mystified" by the claims about school buildings.
"They went through every step of every process required to build a school in Malawi, and the schools were built in the model of schools all across the country," Mr Neilson told the BBC.
Mr Neilson said: "Madonna is the largest individual philanthropist in Malawi. We will continue to fund programmes that support children in Malawi."