At least seven suspected al Qaida members have been arrested over the rocket attack on a diplomatic convoy carrying the deputy British ambassador to Yemen, security sources said.
Fionna Gibb escaped unharmed following the blast in the capital Sana'a on Wednesday morning.
An unnamed British diplomat who was injured was said to be recovering well and may soon leave hospital, according to ambassador Tim Torlot.
Three other people were also wounded in the attack, which has heightened fears for the safety of westerners in the area.
A security source said the suspects were detained in Sana'a on Wednesday,
Mr Torlot said he had visited the injured British official and found him "in good spirits", although suffering temporary hearing problems and injuries to his side and back.
It was the second time in six months that British officials have been targeted.
Mr Torlot escaped unhurt when a suicide bomber wearing school uniform detonated an explosives belt in April.
He told BBC Radio 4's Today programme that the man injured in yesterday's attack was recovering: "I visited him yesterday afternoon. He's fine. He was in good spirits. We hope he will be out of hospital today."
He went on: "I think the threat in Yemen is increasing. Al Qaida has built up a base here, which the government of Yemen is working very hard to tackle. We are not talking about anything on the same scale as Afghanistan and Pakistan yet, and all of our efforts are going into making sure that doesn't happen."