With an estimated value of more than $50m, Saturday's theft of the painting "Poppy Flowers" took place in broad daylight after it was cut out of its frame at the museum.
Faruq Hosni, Egypt's culture minister, said the police were "on alert at the borders and the airports" to try to recover the painting.
"The search is ongoing. We still haven't found the painting," he told AFP news agency.
Al Jazeera's Ayman Mohyeldin, reporting from Cairo, said the the interior ministry has notified Interpol, the international police organisation, of the theft.
"They are afraid that the painting could be taken abroad and sold there," he said.
An early investigation at the museum showed "flagrant shortcomings" in security, the state's al-Ahram daily reported.
Abdel Meguid Mahmud, the prosecutor general, acknowledged that security measures at the museum were "inadequate", branding them little more than "a facade".
"There are 43 security cameras but only seven are working. Each painting is protected by an alarm but again, none are working," he said.
Hosni, the culture minister said he "did not imagine that it was possible to steal a painting from the Mahmoud Khalil museum".
"The museum would have been closed if it had been known the warning system was not working," he told al-Ahram daily.
Security in musuems
Hours after the theft on Saturday, the culture minister announced that the painting had been recovered but he later backtracked, blaming a subordinate for having passed on "inaccurate" information.
Zahi Hawass, Egypt's antiquities chief, has been ordered to co-ordinate with the security services to have alarm systems checked at museums throughout Egypt, newspapers said.
The "Poppy Flowers" Van Gogh painting of yellow and red flowers in a vase had been stolen before, in 1977, but was recovered two years later.
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.