Rome was ready to "reactivate" controls just as it did for the G7 in June, as "a temporary measure to allow Bavaria to reorganize and face the emergency", a statement from the province said.
Bolzano, in the German-speaking Alto Adige region in northern Italy, said Bavaria had asked for "logistical support".
Bavaria's ministry of social affairs said minister Emilia Mueller had met her Bolzano counterpart Martha Stocker on Tuesday, and the latter "offered help".
"We welcome the measures of support announced today. It's a true example of European solidarity," the ministry said.
The region will also take in "between 300 and 400 refugees", housing them temporarily in a number of gyms already equipped for such use, under the organisation of the civil protection agency, and at the cost of the state.
"Bavaria is witnessing record arrivals of refugees, mainly via the Balkan route, which is creating an unmanageable situation," the province said, adding that efforts were underway "to find new structures and cope immediately with the exponential growth in the number of migrants".