"We were informed (on Monday) that one of them was sent to the Office of the President (of Venezuela)," the statement said.
"We hope that things like this will contribute to continue uniting the citizens of two such brotherly and beloved countries like Colombia and Venezuela are," the statement said.
Chavez thanked Shakira for her gift Sunday on state-owned Venezolana de Television.
"Izarra, I didn't know about the guitar from Shakira ... we have to thank her, I got it last night and I tried to play a song," Chavez told Communications Minister Andres Izarra by telephone on the air.
"Shakira sent Pres. Chavez this autographed guitar," Izarra said in a Twitter posting over the weekend that included a link to a photo of the red instrument.
Chavez said during his weekly show on March 27 that the Colombian singer had asked to meet with him but scheduling problems had prevented them from doing so.