Information about the bomber's identity first emerged in the US - with American TV networks CBS and NBC naming Abedi as the suspect.
Ms Rudd was asked whether she would be looking at how information sharing may have resulted in the premature release of details the British police and security services had not wanted in the public domain.
The home secretary told Today: "Yes, quite frankly.
"The British police have been very clear they want to control the flow of information in order to protect operational integrity - the element of surprise - so it is irritating if it gets released from other sources, and I've been very clear with our friends that that should not happen again."
Pressed on whether the Americans had compromised the investigation, she said: "I wouldn't go that far, but I can say they are perfectly clear about the situation and that it shouldn't happen again."
BBC assistant political editor Norman Smith said Ms Rudd's irritation stemmed from the fact "crucial information about the investigation" had been "leaked to the media in the US".
She had been concerned that this "might have compromised aspects of the investigation", namely that it may have "alerted associates" of the bomber "that the security forces here knew who they were looking for".
He added: "Ms Rudd, I'm told, got on the blower to US officials and gave them a piece of her mind. Officials say they are in no doubt about our views on that."