The MoD said it was believed that the three soldiers died in the initial blast.
The troops were carrying out a routine security patrol with Afghan national security forces.
Colonel Richard Kemp, who served as commander of the British army in Afghanistan in 2003, told the BBC: "These soldiers were from 1st Battalion Parachute Regiment which is, as is publicly known, the special forces' support group.
"So they carry out support operations for the special forces. They are not actually special forces themselves."
The 4x4 Jackal has been used in Afghanistan to offer troops better protection than the more lightly armoured Snatch Land Rover, but there have still been a number of fatalities involving the vehicle.
July saw more casualties than any other month for UK forces in Afghanistan, with 22 service personnel killed.
Colonel Richard Kemp: "Getting among the local population... can only really be done on the ground"
Troops are now involved in the second stage of Operation Panther's Claw, which the MoD says is focused on holding ground won from the Taliban in recent weeks.
On Tuesday, Craftsman Anthony Lombardi, 21, of Scunthorpe, from the Royal Electrical and Mechanical Engineers, attached to the Light Dragoons, died in an explosion.
His body has been flown back to RAF Lyneham in Wiltshire, where a private repatriation ceremony took place.
The latest deaths come after new Nato Secretary General Anders Fogh Rasmussen, who is in Afghanistan, said more troops were needed in the country.
He told BBC Radio 4's Today programme: "I have seen progress in the south, not least thanks to the increase in the number of troops. So definitely the number of troops matters.
"However, we also have to realise that there is no military solution solely.
"We have to provide the Afghan people with better life opportunities as well if we are to win hearts and minds, and this will be at the core of our new strategy."
BRITISH ARMY JACKAL
Agile, all-terrain, armoured vehicle used in Afghanistan for reconnaissance, rapid assault, and convoy protection.
A safer alternative to the Snatch Land Rover, it has an armoured hull which provides increased protection from roadside bombs.
Weapons: General purpose machine gun for crew protection. Heavy machine gun or grenade machine gun as main weapon system in fire support role
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.