From Sunday, IPT will increase from 6% to 9.5%, a rise that was announced by Chancellor George Osborne in his Summer Budget.
Motorists renewing a comprehensive policy - or taking out a new one - will face an average rise of £13.
Buildings and contents policies will go up by an average of £10.
But the AA warned that young drivers - and motorists living in London - will be harder hit.
It said drivers under the age of 22 will pay £42 a year more on average, and Londoners will pay £31 more.
But even after the tax rise, car insurance premiums are likely to remain lower than they were three years ago.
Premiums in the third quarter of 2012 were £406 on average, according to the Association of British Insurers (ABI).
In the same quarter this year, the average premium was £379.
However the AA said prices had risen significantly over the summer.
"Already, premiums have risen by nearly 10% over the past six months and the IPT rise will only pile on the misery," said Janet Connor, managing director of AA Insurance.
She also warned that Sunday's increase could encourage some young people to drive without insurance.
Hannah Maundrell, the editor in chief of money.co.uk, said the tax rise was a "drop in the ocean" compared with the amount that consumers could save by changing to another provider.
She said drivers, for example, could save up to £223 a year by switching.
Those affected by the tax rise include:
However travel insurance will not be affected, as the higher IPT rate of 20% remains unchanged.
Life policies and mortgage insurance are exempt.
The increase will raise an extra £1.5bn a year for the Treasury by 2017/18.
Millions of people face a rise in their insurance bills this week-end, as a result of an increase in Insurance Premium Tax (IPT).