Amnesty said the decision was made after doctors advised against this week's 50 lashes on health grounds.
Mr Badawi was sentenced last May to 10 years in prison and 1,000 lashes for "insulting Islam" and disobedience.
He was due to receive the lashes over 20 weeks and was given the first round on 9 January.
Footage that emerged of that flogging showed the slight figure of Mr Badawi standing in a white shirt as he was beaten with a stick.
Ensaf Haider, the blogger's wife, said she was "relieved" he would not be flogged again on Friday, but said she remained concerned about his health.
The BBC's Middle East analyst Sebastian Usher says Mr Badawi's sentence provoked international outcry on a scale that Saudi leaders may not have been prepared for.
The question is whether the Saudis will still carry out the full punishment after this second postponement, our correspondent adds.
Earlier this week, the BBC learned that Mr Badawi's case had been referred to the Supreme Court by the king's office.
Saudi Arabia has postponed the flogging of blogger Raif Badawi for the second week running, according to human rights group Amnesty International.