When he left the country last month, Liberian national Thomas Eric Duncan filled in a questionnaire saying that none of his relatives were sick.
But Liberia’s assistant health minister said he had taken a sick relative to a clinic in a wheelbarrow.
Mr Duncan is in a serious condition in a Dallas hospital.
His is the first case of Ebola to be diagnosed on U.S. soil, where as many as 100 people are being checked for exposure to Ebola.
More than 3,330 people have died in the Ebola outbreak in four West African countries.
The prosecution announcement was made at the weekly Ebola update news conference, which is attended by numerous government officials and was dominated by the case of Mr Duncan.
Liberia has been worst-affected by the outbreak with 1,998 deaths recorded in the latest UN figures
“We wish him a speedy recovery; we await his arrival in Liberia” to face prosecution, Binyah Kesselly, the chairman of the board of directors of the Liberia Airport Authority, said.
Deputy Information Minister Isaac Jackson confirmed that Mr Duncan would be prosecuted as he “lied under oath about his Ebola status”.
Before the briefing, Mr Kesselly told the BBC that Mr Duncan had answered “no” to all the questions on the Ebola form, which includes one about whether the traveller has any relatives sick with Ebola.
Assistant Health Minister Tolbert Nyenswah explained at the briefing that he was investigating Mr Duncan’s movements before he left Liberia on 19 September.
A British nurse told a UK conference on Thursday of “the horror and misery” of death from Ebola in Sierra Leone
He said Mr Duncan works as a driver in Liberia for Save-Way Cargo, a subsidiary of the international courier service FedEx, and lives in the Paynesville 72nd Community suburb of Monrovia.
Eric Vaye, a neighbour of Mr Duncan’s, was also at the briefing to help with contact tracing, and said that nine people had died of Ebola in the district in recent weeks.
According to the latest UN figures, there have been 7,178 confirmed Ebola cases, with Sierra Leone, Liberia and Guinea suffering the most.
A Liberian, Patrick Sawyer, brought Ebola to Nigeria on July 20. He died on July 25 taking along seven others.
The country has managed to contain the virus with the last confirmed case recorded on September 5.