"I feel like I am working alone and that I alone spend time thinking of how to manage cultural affairs," the minister Farouk Hosni told daily newspaper al-Masry al-Youm on Tuesday.
"I can't work with these incompetent employees," he said. "I'm tired and I can't sleep, because I wake up in the middle of the night fearing for the artefacts and the museums."
The painting, known as "Poppy Flower" according to a statement in Arabic, was stolen on Saturday morning from Cairo's Mahmoud Khalil Museum, home to one of the Middle East's finest collections of 19th- and 20th-century art.
The museum houses works assembled by Mohammed Mahmoud Khalil, a politician who died in 1953, including paintings by Gauguin, Monet, Manet and Renoir, as well as the Dutch post-Impressionist master Van Gogh.
An early investigation of the theft showed "flagrant shortcomings" in security, with only seven out of 43 security cameras working properly , state media said.
Hosni, an abstract painter who has held the culture brief since 1987, said staff at the museum were guilty of negligence.
"The painting would have been stolen even if there were a thousand surveillance cameras, because of the negligence of the museum staff," Hosni was cited as saying by Al-Akhbar newspaper.
The culture ministry's head of fine art, Mohsen Shaalan, has been detained along with four other officials pending investigation for 19 days after being accused of "negligence and failing to carry out their employment duties".
Nine other employees were barred from travel.
Hosni said the ministry would create a central control room to monitor all museums, supervised by his cabinet, and set up a committee to review surveillance of museums across the country.
"We are currently setting up an additional 18 museums and they will all be supplied with state of the art security sensors against theft and fires," Zahi Hawass, secretary general of the Supreme Council of Antiquities in Egypt, said in a statement.