Abhisit Vejjajiva, the prime minister, called an emergency meeting of security officials following the blasts.
Al Jazeera's Wayne Hay, reporting from Bangkok, said: "We heard explosions right in a busy tourist and restaurant area.
"Certainly the situation has the potential to get a lot worse."
So-called 'multi-colour' protesters have been holding a demonstration in the area recently, and are camped a few hundred metres from where the blasts took place in a heavily guarded area.
They have been calling for anti-government red shirt demonstrators to end their protest against the government.
The red shirts have been camped out on the streets of Bangkok since March 12, with the stand-off causing widespread disruption, closing shopping malls, hotels and causing millions of dollars in losses for Thailand's vital tourism industry.
The red shirts consist mainly of poor rural workers and pro-democracy activists who opposed the military coup that ousted Thaksin Shinawatra, the then prime minister, in 2006.
They want parliament dissolved immediately and new elections called, saying the current government is illegitimate.
A report in The Nation newspaper on Thursday said red shirt leaders were insisting on an immediate dissolution of parliament and had rejected an appeal by a national economic council to wait until a budget bill was passed in July.
|Thai officials say an M79 grenade launcher was used in the attacks [AFP]
Aela Callan, Al Jazeera’s correspondent in the Silom area, said that such small M-79 grenades had been used on government buildings around Bangkok in recent months.
She said that very quickly after the blasts the army had spoken on loud speakers in the area and blamed the red shirts for the attacks.
"Many fear that it has set up the situation for a crackdown on the red shirts," she added.
The red shirt leaders have condemned the attacks.
Some leaders of the red shirts had previously suggested they might consider a three-month timeframe for Vejjajiva to dissolve parliament and call elections.
The multi-colour protesters have said that they are not alligned to any side but are purely against the red shirts.