Footage from North Korean state television showed Richardson and Schmidt at the Pyongyang airport on Monday evening.
"We are going to ask about the American who's been detained. A humanitarian private visit." Richardson said.
The delegation comprised Schmidt, his daughter, Richardson and Google executive Jared Cohen, according to South Korean news media and it arrived in Pyongyang on a flight from the Chinese capital, Beijing.
The mission has been criticized by the White House due to the sensitivity of the timing. The United States does not have diplomatic relations with North Korea and the isolated and impoverished state remains technically at war with South Korea.
South Korea is in the midst of a transition to a new president who will take office in February, while Japan, another major U.S. ally in the region, has a new prime minister.
A U.S. official said the trip's timing was particularly bad from the Obama administration's point of view because it comes as the U.N. Security Council ponders how to respond to North Korea's December 12 missile launch.
"We are in kind of a classical provocation period with North Korea. Usually, their missile launches are followed by nuclear tests," said the official, who spoke on condition of anonymity.
"During these periods, it's very important that the international community come together, certainly at the level of the U.N. Security Council, to demonstrate to North Korea that they pay a price for not living up to their obligations."
Richardson, a former ambassador to the United Nations, has made numerous trips to North Korea. The reasons for Schmidt's involvement in the trip are not clear, though Google characterized it as "personal" travel.
Schmidt did not respond to requests for comment.
Richardson's efforts to seek the release of Kenneth Bae, a Korean-American tour guide who was detained last year will mark the latest in a series of high-profile visits to free detained Americans in Pyongyang.
Richardson told CBS television last Friday that he had been contacted by Bae's family and that he would raise the issue while in North Korea.
Pyongyang's most notable success was securing a visit from former President Bill Clinton in 2009 to win the release of two American journalists.
Last year, Jared and Schmidt met defectors from North Korea, a state that ranks bottom of Reporters Without Borders annual survey of Internet and press freedom.
Media reports and think tanks say that officials from the North Korean government went to Google's headquarters in 2011, something the U.S. technology giant declined to comment on.