Shalit was spotted taking a walk near his Mitzpe Hila home with his mother, Aviva Shalit, and military mental health officials, Haaretz reported.
News of a visit by five army doctors to Shalit's home came after reports Tuesday he didn't feel well during a flight from Egypt to an Israeli military base despite an initial examination that pronounced him in good health, Haaretz said. At the base, Shalit underwent a more thorough exam before officials sent him home under medical supervision.
Shalit's father, Noam Shalit, said his son "is doing well and he slept well overnight."
"He needs quiet to recuperate and we hope to return to a normal life as soon as possible," the father said.
In exchange for Shalit, Israel freed 1,027 Palestinian and Israeli Arab prisoners. Shalit was a 19-year-old corporal when he was kidnapped and taken into Gaza by Hamas and other Palestinian militants in a cross-border raid in June 2006.
Since Hamas signed the prisoner swap agreement with Israel, senior Hamas official Mahmoud Zahar challenged Palestinian Authority President Mahmoud Abbas to test his popularity in elections, Gaza newspaper al-Resalah reported.
"We invite [Abbas] to enter into elections to see the extent of his popularity in the Palestinian street," Zahar said.
Zahar dismissed criticism of the Shalit deal could have undermined the reconciliation agreement between Hamas and Fatah, which Abbas has said he pursued to allow for national elections, turning the criticism to Abbas, The Jerusalem Post reported.
"Abbas disrupted the reconciliation under U.S. pressure for the benefit of [the U.N. statehood bid in] September," Zahar said.