As the princess stood next to survivors of concentration camps at an event to mark Holocaust Memorial Day, SVT reporter Rolf Fredriksson asked her: "Has the Crown Princess thought about family history?" and mentioned that some of her relatives were known to support the Nazis.
"Nazism is something horrific. It is one of humanity's absolute worst periods," the princess responded, choosing not to mention her family.
In a separate comment, the Crown Princess said: "We must not forget what we can learn from history. It is important that we gather here, that we remember and listen to stories and pass them on."
Margareta Thorgren, chief press officer for the Royal Court later told Swedish newspaper Expressen that it was "absolutely the wrong time to ask that question."
"It was disrespectful to the two survivors who stood next [to her] in the freezing cold," she added.
The Crown Princess's grandfather Walther Sommerlath, a German businessman, is understood to have been a member of the Nazi party, although he denied it when questioned by the Swedish media during the 1970s, saying that his main role during the Second World War was working at an arms factory in Berlin.
Holocaust Memorial Day events took place around the world on Tuesday as people came together to mark the 70th anniversary of Jews and other prisoners being freed from Nazi extermination camps in Poland.
After SVT's broadcast from Auschwitz, Twitter was flooded with comments from people questioning its reporter Rolf Fredriksson's judgement.
Anne Ramberg, Secretary General of the Swedish Bar Association described his decision as "tasteless".
But others praised his interrogation, including Swedish author Göran Greider who described the questioning as "strong" and "unexpected".
Fredriksson responded to the criticism with his own post on Twitter, saying he had a "responsibility" to discuss the issue and praising the Crown Princess for being a "committed anti-Nazi".
On Wednesday afternoon, as the Twitter backlash against him continued to grow, he posted: "History is my favourite subject, and it needs to be constantly discussed."