Officials said cables were also severed twice last week causing massive disruption to businesses in the impoverished country.
"We are investigating the cable cutting incident which took place today (Tuesday) with high priority," said Ziaur Rashid Sofder, general manager of security at the Bangladesh Telephone and Telegraph Board.
"We are taking it very seriously because it was a really big sabotage," he said, adding that three people were arrested last October following a similar attack.
"They confessed that someone had given them money to cut the cable but police are still investigating the incident," he said.
Azahar Chowdhury, vice president of Internet Service Providers of Bangladesh, said the sabotage had prevented all Internet use and international telephone calls for most of Tuesday.
Other industry figures called for urgent action to prevent further problems.
"We were completely detached from world communications -- it was total isolation, a complete disaster," said M