Foundation for Peace represents those affected by the 2005 attacks, where suicide bombers killed 52 people and injured more than 770 in London.
The exhibition features artefacts belonging to the Met's Crime Museum.
The force said displaying such items was "always going to be" complex.
Items from historic and recent crimes are displayed at the exhibition in the Museum of London.
Nick Taylor, chief executive at the Foundation For Peace said people affected were living with the "physical and mental consequences" of the 7/7 terrorist attacks every day.
He said trauma manifests itself in different ways and "anything like this" can act as a trigger for post traumatic stress.
He added: "People may not able to go out or get dressed, they may feel depressed and not be able to go out to work - or even be able to do normal tasks we take for granted, like getting up in the morning."
Acts of terrorism could traumatise victims a long time after the event, he said, so 10 years since the attacks did not mean people were not still struggling.
Met Police assistant commissioner Martin Hewitt said the exhibits gave insight into the force's detective work and were "fascinating stories".
He added: "We have used an ethical panel to scrutinise and discuss the proposed selection to ensure that we are sensitive to both the victims and the officers involved, and their families.
"Under no circumstances did we want the museum to glamorise crime, or the criminals involved."
Replicas of the rucksacks used to plant bombs in the 7/7 attack on display may trigger post traumatic stress in survivors, according to a charity.