The two first ladies than traveled to Jubilee House, Ghana's presidential palace, for a private meeting.
Mrs Melania Trump also donated a photo therapy machine to the hospital, which will be used to treat jaundice.
Melania said she was looking forward to visiting "four attractive and very different countries" in Africa prior to her visit.
She was met by her Ghanaian counterpart Rebecca Akufo-Addo and a group of local schoolchildren in yellow and brown uniforms waving the USA stars and stripes and the Ghanaian flag.
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He says all these positive things about us and all these nice things about me is nice but it is tactics, it starts already. We want to play an attacking game and we've got to bear their characteristics in mind. "I like Carlo Ancelotti ".
Dancers performed in the capital city of Accra for the first lady and she seemed to enjoy the moment, clapping to show her appreciation. She later joined Akufo-Addo for tea.
Her husband, Donald Trump, caused anger in January when he reportedly disparaged some African states and Haiti as "shithole countries".
The president has denied making the comment. Would she offend a whole nation with one pair of shoes? anything was possible - but we didn't expect her to kick off her trip by weighing in on one of fashion's most heated conversations.
Stephanie Grisham, the first lady's spokeswoman, said the trip is consistent with both first lady's platform and Trump administration policy, noting that the president has said, "The U.S.is the world's largest giver of foreign aid".
Trump has focused on children as her signature issue and plans to promote child wellbeing during her four-country tour.
USAID and the U.S. Department of State provided more than $8 billion in assistance to 47 countries in sub-Saharan Africa in 2015.