Facebook users going through such servers are violating the law, she said responding to a question from journalists on Sunday before a meeting at the Secretariat.
"Firstly, using the proxy servers is a breach of the law. Those who are using them are using a bandwidth with a specific capacity. They won't be able to do that much longer. Because this bandwidth's capacity is low."
"The second bandwidth's speed is far lower than normal. Saboteurs can't communicate and organise attacks fast enough using that bandwidth. It's very easy to track (anyone's internet activity) if the speed is low."
She warned those accessing Facebook through proxy servers, saying, "They should know that their IDs can be hacked and it's highly possible (that this will happen)."
The minister said Facebook could not be blocked completely without shutting down the internet.
"I ask you (journalists) to find out whether it's possible or not. I hope you will find the answer. Closing down Facebook 100 percent is not possible in any country in the world, not even where the Facebook admins live."
Bangladesh government made Facebook, Facebook Messenger, Viber, WhatsApp and several other messaging and calling apps inaccessible since Nov 18 on the grounds of national security.
It has given no indication as to when the ban will be lifted. Meanwhile, many have been using Facebook through other proxy sites.
"I think Facebook can't be closed unless the internet is shut down. We don't want to do that. We won't shut down the internet," said Tarana Halim.
She said the authorities were tackling technology with technology. "It's not like the government wants to deliberately keep these apps inaccessible. We should all help each other."
The state minister said they had written to Facebook Inc to ink an agreement to prevent posting of “objectionable” contents on the social networking site.
"We've asked them to place an admin here (Bangladesh). Initiatives have been taken to strike the deal."
Asked when access to the social networking site would be allowed again, she said, "When the home ministry and law-enforcing agencies feel it’s safe."
Posts and Telecommunications Division Secretary Md Faizur Rahman Chowdhury at Sunday's meeting said 'all intelligence agencies are running a surveillance on those accessing Facebook via proxy servers'.
"We are only catching only those that need to be caught, not everyone."