She said her trip would take her to "four attractive and very different countries in Africa".
Trump later had a private meeting with first lady Akufo-Addo.
The "Be Best" initiative was launched earlier this year to focus on overall child well-being with an emphasis on opioid addiction and online behaviour. She arrived in the West African nation on Tuesday and visited a baby clinic.
She also watched a nurse demonstrate how vitamins are administered to babies by mouth and toured the neonatal intensive care unit.
"So looking forward to visiting Ghana, Malawi, Kenya & Egypt as I take BeBest global", Trump posted to Facebook Tuesday. Mrs. Trump's plane touched down at Ghana's Kotoka International Airport, KIA, on Monday morning.
Locals who spoke with reporters in Accra said they did not know much about Trump's visit. "I don't think I have ever heard her name, Melania".
The African tour is a favourite among U.S. first ladies. She later joined Akufo-Addo for tea.
Several of the first lady's moves have been interpreted by the media and public as slights toward her husband.
Before this week, the phrase "Trump trip to Africa" might have meant a big-game hunting excursion with Donald Jr. and Eric.
"Why are we having all these people from shithole countries come here?" the president reportedly said, apparently also asking why more "people from countries like Norway" don't come to the USA instead.