She said the Australian delegation to the summit "should not be headed by Mr. Abbott as prime minister." Abbott's office did not immediately respond to the incident on Monday.
Human rights group Amnesty International said Rhiannon's detention confirms a pattern of continuing human rights abuses in Sri Lanka.
The APNZ news service reported that Logie said she was safe after her detention.
The decisions by the Indian and Canadian leaders to not attend the summit is expected to sharpen the focus on demands by Western nations and rights activists that Sri Lanka account for thousands of civilians who are suspected to have died in the final months of a quarter-century civil war that that ended in 2009 when government forces crushed separatist Tamil rebels.
Singh sent a letter to Sri Lankan President Mahinda Rajapaksa expressing his inability to attend the summit, said Syed Akbaruddin, the External Affairs Ministry spokesman. He did not divulge the contents of the letter.
External Affairs Minister Salman Khurshid will represent India at the summit, Akbaruddin said.
India, which has a major interest in the issue because southern India is home to 60 million Tamils, has been urging Sri Lanka's government to resume negotiations with an ethnic Tamil party on increased local autonomy for Tamils.
After the war, Rajapaksa promised to allow a greater degree of autonomy in Tamil-majority regions in the north. However, he has been criticized by foreign countries and rights groups for failing to deliver on his promises.
Harper said last month that Canada was disturbed by ongoing reports of intimidation and incarceration of political leaders and journalists, harassment of minorities, reported disappearances and allegations of extrajudicial killings.