Police said there were no injuries and they were investigating whether the blasts were linked to a string of letter bombs intercepted in the country since early January.
An employee in the Amsterdam sorting office heard a hissing sound as they were about to open a letter, the city's police said. "The employee threw the letter away and there was a small explosion," the force added on Twitter.
ABN's chief executive, Kees Van Dijkhuizen said he had spoken to the man who had handled the letter at the sorting center in the western outskirts of the city.
"Good news is that he is not wounded, bad news of course is that these things happen and that our people have to deal with it," Dijkhuizen told journalists.
The second explosion in the southern town of Kerkrade, on the border with Germany, was at the offices of Ricoh, a Japanese electronics company.
"Thankfully there were no injuries, but those involved are of course very shocked," Ricoh said in a statement cited by Dutch media. It caused some damage, and the facility was closed for forensic analysis, police said.
Dutch police have been investigating a spate of letter bombs since Jan. 3, which they said appeared to have been sent by the same person. They were all intercepted before they could go off.
Previous targets have included a hotel, a gas station, a garage, a real estate agent and a bill collection service.
Comment: Another bomb went off the following day, at an ING bank in Amsterdam. No one was killed there either.
They're currently suggesting some kind of 'BitCoin extortion plot' is afoot.