Hundreds gathered outside the National Bardo Museum in central Tunis, many carrying placards encouraging foreigners to visit Tunisia which relies heavily on tourism income.
The museum's head of communications told AFP plans to reopen to the public today were scrapped "at the last minute".
"The interior ministry says that for security reasons we cannot receive a large number of visitors," Hanene Srarfi said.
Museum officials had planned to reopen today, six days after an attack claimed by the jihadist Islamic State (IS) group killed 20 tourists and a policeman.
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Several events had been planned for today to protest against the attack, with hundreds of people demonstrating outside the museum.
Some held signs in English reading "Visit Tunisia", while others carried banners that said "I will receive you with jasmine".
"If we want tourists to come back we must set an example," demonstrator Najet Nouri said.
A handful of tourists arrived at the Bardo unaware that the reopening had been postponed.
"We were not told. We came here to visit the museum," French tourist Eliane Cotton told AFP.
A culture ministry statement said there had been "logistical" problems in readying the museum for an anticipated "thousands of people".
The authorities announced at the weekend the Bardo would reopen today, less than a week after the deadly rampage.
Museum directors said they wanted to resume normal operations as soon as possible to show that the gunmen "had not achieved their objective".
Officials have admitted there were security failures on the day of the attack on the complex, which is next to Tunisia's parliament.