A statement from the ministry's population and immigration authority said the measure would apply to migrants currently at the southern Holot detention centre, "who infiltrated Israel and cannot be expelled to their country of origin".
There are currently around 2,000 African migrants at Holot out of an estimated 42,000 in Israel.
Most of the migrants at Holot hail from Sudan and Eritrea and would face danger were they to return home.
Israel will identify migrants who qualify for the measures, inform them of the proposed destination, and pay for their plane ticket and hotel there.
A spokeswoman for the interior ministry refused to name the third-party countries, but media and some charities named them as Rwanda and Uganda.
"An infiltrator who agrees to this procedure will begin the preparations for leaving, an infiltrator who refuses will face a hearing following which it will be decided whether they will be imprisoned," read the statement, released Tuesday.
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Interior Minister Gilad Erdan said the measure would "encourage infiltrators to leave Israel in a safe and dignified way, and will be an effective tool to upholding our committment to return life to normal in Israel".
Most African migrants in Israel reside in impoverished areas in southern Tel Aviv, where their presence has triggered protests from veteran residents.
The interior ministry said the measure has been approved by Israel's attorney general, and was to come into force "in the coming days."
In a joint statement, six local and international rights groups protested the measure, which they said was "illegal".
The groups said that Rwanda and Uganda are not safe and that migrants who arrive there are stripped of their cash and documents. They demanded Israel expose any agreements it had made with those countries.
Israel has previously offered cash stipends to African migrants in return for them leaving the Jewish state.
The interior ministry said that since last year, 1,500 migrants "wilfully left to a third country, in addition to 7,000 who left for their country of origin".