Any assets held in Britain by the group which kidnapped and murdered British engineer Ken Bigley are to be frozen.
The Treasury says the move is not a direct response to Bigley's death
Chancellor Gordon Brown told the Bank of England to give the order to all financial institutions on Thursday.
Mr Brown told MPs: "We must do all in our power to ensure there is no hiding place for terrorists and no hiding place for those who finance terrorism."
It is not known whether the Tawhid and Jihad group, led by Jordanian militant Abu-Musab al-Zarqawi, have UK funds.
The group last Friday admitted killing British hostage Kenneth Bigley, who was held hostage for three weeks.
A $25m reward is being offered for information leading to the capture of al-Zarqawi.
His group on Thursday claimed responsibility for two explosions, thought to be suicide attacks, inside Baghdad's heavily fortified Green Zone.
The order makes it a criminal offence for any financial institution to deal in any way with funds held by the group and any existing funds cannot be released.
Treasury sources say it is impossible to know whether the group has any funds in the UK, although that was something which might be revealed as the freezing orders are sent to more than 600 banks.
However, it is thought the impact in Britain may be small.
About 100 freezes on individuals and similar groups, including al-Qaeda, the Real IRA and Hamas, since 11 September 2001 have only netted between £500,000 and £1m in the UK, the BBC's James Robbins says.
But the government hopes other countries will also impose the measure so the group is eventually listed by the United Nations as a banned terrorist organisation, as has happened with al-Qaeda.
Mr Bigley was paraded before the world before his death
It would then be illegal for the group to hold funds or raise money anywhere
in the world.
Around $130 and $150m have been stripped away from terrorist organisations around the world since the 11 September terror attacks.
However some experts believe the impact will still be limited as many terrorist groups do not use the usual banking channels subject to such measures.
Paul Rogers, professor of peace studies at Bradford University, said as international organisations tried to curb terror groups' finances, they often found new informal channels.
But there were still suspicions some funds were lodged at formal banks, Prof Rogers told BBC Radio 4's PM programme.
A Treasury statement said: "Chancellor Gordon Brown today instructed the Bank of England, as agent for Her Majesty's Treasury, to direct financial institutions that any funds which they hold for or on behalf of the group Jama'at al-Tawhid Wa'al-Jihad (JTJ) must be frozen with immediate effect."
Mr Brown told MPs they had publicly admitted Mr Bigley's murder as well as perpetrating a range of terrorist acts in Iraq.
"Following our discussions, we are working with international partners to deny JTJ access to funds across the world," he added.
The chancellor is using measures agreed at the United Nations in 2001.
Increased support for al-Qaeda and its associates in recent years, partly due to anger at the Iraq war, had increased such support, he suggested.
Thursday's order is not in directly response to Mr Bigley's death, say officials. Instead, there has been a long legal process to ensure the group can be formally classed as a terrorist organisation.