The decree follows a government investigation into the UN report about prisoner abuse, which found detainees were tortured at the time of arrest and during interrogations.
"Relevant authorities are required to equip the intelligence and investigating agencies... with modern equipment (and) devices... and videotape the interrogation process," Karzai said in a decree released by his office late on Saturday.
He said the move will also help "eliminate any chance or place for complaints from other parties" about prisoner abuse.
The United Nations, which has run an assistance operation in Afghanistan since the 2001 fall of the Taliban, said in January that prisoners were frequently abused and tortured in the Afghan jail system.
The UN report revealed that 326 of 635 prisoners interviewed across the country said they had been abused, including 80 minors.
Fourteen types of torture were described in the UN report, including beatings with cables and pipes, attacks on the genitals, threats of execution or rape, electric shocks and forced stress positions.
In the decree, Karzai also ordered the attorney general to "prosecute the perpetrators of torture, so to avoid any suspect, convict or prisoner tortured in the future".
The decree strictly orders law-enforcement bodies, police and the intelligence agencies to avoid torturing detainees. Karzai also orders his justice minister and the court systems to provide defence lawyers to prisoners.
Afghanistan has been in near-continuous war since the late 1970s, the last 11 years a Taliban-led Islamist insurgency being fought by a US-led NATO force that currently numbers more than 100,000 troops.