According to the minister, Zimbabwe in 2011 spent $14.8m on its 3 000 schools, excluding salaries.
President Robert Mugabe and Prime Minister Morgan Tsvangirai, along with their officials, racked up $45m in travel expenses abroad, Coltart told dpa.
"It's shameful," Coltart said. "The infrastructure in our schools is in crisis. We are undermining the education of an entire generation."
Coltart is a member of Tsvangirai's Movement for Democratic Change party, which has been in an uneasy coalition with Mugabe's Zanu-PF party since 2009.
Finance Minister Tendai Biti, also from the MDC, had revealed previously that Mugabe's trips - with delegations of up to 80 people - cost the country $20.6m last year. He says he is powerless to contain the president's travel.
Government officials are also accused by Zimbabwean watchdogs of going abroad for shopping sprees at taxpayers' expense. The 88-year-old president, believed to be recovering from cancer, frequently travels to the Far East for medical treatments.
After independence in 1980, Zimbabwe, led by Mugabe - who was a school teacher before becoming a liberation fighter - built up its education system to be one of the best in Africa.
But the country is only now starting to recover from an economic collapse in 2008 - when inflation hit 500 billion percent. The national currency crashed and government services ground to a halt. Schools were shut down for much of the year.
Economists say Mugabe's policies of the last 15 years, including the seizures without compensation of white-owned farms, caused the tailspin.
Last year, Western governments pumped $24m of aid into Zimbabwe's schools, including a programme to provide 523 million textbooks for pupils.