According to Rasmussen, authorities in the Gulf country took the politician's passport while he was detained, citing a security risk.
He had travelled to Bahrain to visit Danish citizen and human rights activist Abdulhadi al-Khawaja.
Al-Khawaja is, according to Rasmussen, seriously ill in prison. The Danish MP's visit was intended to put pressure on Manama to provide the Danish-Bahraini dual citizen with necessary medicine.
But Rasmussen was neither permitted to enter Bahrain nor visit the prison where al-Khawaja is held.
He informed Ritzau on Thursday morning that he had been sent out of the Middle East country and was in Istanbul, waiting for a connecting flight to Copenhagen.
“I had hoped to be able to visit him in prison. I expected to be able to enter the country. I had certainly not imagined that I as a member of parliament would have my passport confiscated and be harassed in this way,” he said.
The MP added that he considered the incident to further confirm a serious breach of human rights in Bahrain's prisons.
“It may be assumed to be correct that [al-Khawaja] is being treated poorly, as it would otherwise have been no problem to let me into the country. This is an attempt to hide things and harass those who want to speak about the criticisable human rights situation in Bahrain,” Rasmussen said.
Although Danish foreign ministry representatives regularly visit al-Khawaja, the Social Democrat MP said this was not enough.
“He is still in prison, now for the seventh year. So it's time a Danish politician tried to go there,” he said.
Al-Khawaja is the founder and former leader of both the Gulf Center for Human Rights (GCHR) and the Bahrain Center for Human Rights (BCHR).
He lived in Denmark for 12 years before returning to the Gulf country in 2001. In 2011, he was sentenced to life for conspiring against the nation's Sunni monarchy in the wake of majority Shiite protests.
The small kingdom of Bahrain has since 2011 cracked down on Shia representatives demanding reforms.
Human rights organisations repeatedly accuse the oil-rich Gulf country of suppressing all forms of opposition.