Mr Salmond linked the police complaint by Yes Scotland to the scandal over phone hacking which sparked government inquiries on both sides of the border.
"It's a very serious matter indeed," he told STV News.
"There is a limit to what we can say because obviously it is now a police inquiry.
"But what I would say is that if it turns out, and of course it has still to be determined, that a newspaper has been involved in some way, given everything that has happened over the last few years with illegal hacking and the whole scandal that erupted from that, if that turns out to be the case then it would be a very serious matter indeed."
Yes Scotland has filed a police complaint after private emails were allegedly accessed.
The pro-independence group contacted BT after it received a media inquiry last week that appeared to contain information from internal correspondence, according to reports.
Police Scotland said the matter was under investigation. A spokeswoman said: "A complaint has been made by Yes Scotland regarding unauthorised access to an email account. The matter is being looked into."
A Yes Scotland spokesman said: "We can confirm that a complaint has been made to Police Scotland regarding unauthorised access to Yes Scotland email."
Lord Justice Leveson led a UK government-commissioned investigation into media abuses which outlined a blueprint for tougher media regulation.
A Scottish Government-appointed panel later recommended a mandatory press regulator backed by law.