"If the enemies infiltrate our press, this will be a big danger to the country's security and the people's religious beliefs. I do not deem it right to keep silent," the leader said.
Reformist deputies staged a brief walkout.
The press law was passed by the last conservative-dominated parliament, and has been used to close more than 20 independent newspapers that sprang up after the election of the pro-reform president, Mohammad Khatami, in 1997.
Amending the law was a key campaign pledge of the reformers, who took a majority of seats in elections earlier this year.
Decision 'illegal'
The debate was called off and suspended indefinitely by Mr Karroubi after he read out a letter from Ayatollah Khamenei.
"If the enemies infiltrate our press, this will be a big danger to the country's security and the people's religious beliefs. I do not deem it right to keep silent," the leader said.
"The present press law has succeeded to a point to prevent this big plague. The (proposed) bill is not legitimate and in the interests of the system and the revolution."
One pro-reform deputy, the head of the Press Guild, Rajabali Mazrouie, denounced the decision to block the debate as illegal.
Mr Karroubi justified his decision by reminding deputies that the constitution contained "elements of the absolute rule of the supreme clerical leader".
The official Islamic Republic News Agency (IRNA) reported that the speaker's decision triggered disputes "which led to physical encounters in some cases".
Cleric arrested
Since 1997 hardliners have lost considerable power, but they still retain control over the judiciary, military and broadcasting.
As supreme leader, Ayatollah Khamenei has the last say in key matters of state.
On Saturday a leading Iranian pro-reform cleric, Hasan Youssefi Eshkevari, was arrested on charges of acting against national security and insulting Islamic values.
Mr Eshkevari's outspoken defence of the separation of the state from religion had angered the conservative establishment.