Human rights organisations, leftwing opposition politicians and some media condemned the decision as racist, while rightwing supporters said the soldiers should instead help disadvantaged Israelis.
Commanders of some units in the army, one of Israel's most important institutions, encourage their troops to carry out educational or fun initiatives with the children of African migrants, including in public parks in south Tel Aviv where many can be found.
Ultra-nationalist Lieberman, however, in recent days ordered the army to curtail such activities.
"Lieberman's directive derives from the belief that IDF (Israel Defence Forces) soldiers should take part in activities that are widely agreed upon and not at the heart of public debate, especially when the activity is among a population that is not here legally," a spokesman explained.
"The minister thinks that... IDF soldiers should follow the principle that 'charity begins at home' and help Holocaust survivors, people in need, the elderly," Lieberman's spokesman told AFP.
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"Soldiers must primarily help the needy" Israelis, deputy defence minister Eli Ben-Dahan, a member of the religious nationalist Jewish Home party, told Israeli radio.
Nava Boker, a parliamentarian from Prime Minister Benjamin Netanyahu's ruling Likud party, said "the role of soldiers is to defend the country's inhabitants."
But Tel Aviv Mayor Ron Huldai responded on army radio that the country could "under no circumstances ignore the plight of children living among us."
And former defence minister Amir Peretz of Labour suggested Lieberman should "read a few things about how the Jewish tradition compels us to treat foreigners".
For the leftist daily Haaretz, Lieberman had set "a new record for racism, abominable morals and cruelty".
According to the interior ministry, Israel is home to some 41,000 asylum seekers from Africa.
The vast majority are Eritrean and Sudanese who entered illegally via the Egyptian Sinai peninsula.