Francisco Vidal, the interior minister, said US Ambassador Craig Kelly informed Chile of the request made by Lucia Pinochet Hiriart, who arrived in Washington earlier in the day but was denied entry because of an arrest warrant for her in Chile.
Vidal appeared upset about the surprise request by Pinochet's daughter, who faces charges of tax evasion and using a false passport in Chile.
"Chile is a democratic state, a state of law, where all citizens are assured of a just trial," the minister said.
Lucia Pinochet flew to Washington from Argentina, where she had travelled on Sunday, hours after she was due to appear before court officials to be served notice of her indictment.
Osvaldo Puccio, a Chilean government spokesman, said Pinochet Hiriart, 64, was detained two days after the authorities brought charges against her related to secret multi-million-dollar bank accounts held by her father and his family.
Hiriart, her mother and three of her siblings were charged with fraud on Monday, but Chilean police said Pinochet's eldest daughter had left the country by car the same day.
All could face prison sentences if found guilty.
Pinochet, now 90, and his family are believed to have had $27 million in secret overseas bank accounts in the US, Switzerland and Panama.
The charges relate to the failure to declare at least $8 million, according to legal sources in Santiago.
Pinochet himself was hit with similar fraud charges over the accounts in November.
All the Pinochets, save the elder son, Augusto, have now been charged over the secret accounts and allegations of tax evasion.
Pinochet and family are alleged
to hold $27m in secret accounts
After being charged and put under house arrest on Monday, Pinochet's wife, Lucia Hiriart, and three of their children, Marco Antonio, Jacqueline and Veronica, were granted their liberty while the charges against them are processed.
The family patriarch also faces a barrage of legal challenges, mainly seeking his prosecution, on alleged rights abuses committed under his 1973-1990 dictatorial rule.