The sketch, which starred comedian Atle Antonsen, imagines how it came about that Norway's founding fathers added a notorious clause outlawing Jews from the country to the 1814 constitution.
"It is shocking and embarrassing to create humour from this clause which shut the Jews out of our country!" Dagrun Eriksen, deputy chairman of the Christian Democratic Party, said on Sunday night as the sketch was broadcast on NRK.
"The Jewish clause is part of our dark history," she told VG later, adding that the events remained "painful" for Norwegian Jews.
"As a nation, we must take responsibility for this, and not make flippant skits out of it," she said.
Charlo Halvorsen, entertainment editor for NRK, rejected the criticism of the programme, which was part of the channel's coverage of the start of celebrations of the bicentenary of the constitution on Sunday.
"She is interpreting the sketch in the opposite way to what was intended," he said. "We are ridiculing the people who wrote the paragraph, not the Jews."
"This also happened 200 years ago, and I think it must be allowed to make humour of it," he told VG.
The clause prevented Jews from entering the Kingdom of Norway from the signing of the constitution in 1814 until 1851.
For Norwegian speakers, the offending sketch is below: