The 29-year-old - who joined Newcastle on loan from Sparta Prague in January - is one of three goalkeepers in Ján Kozák's squad for the matches against the Netherlands and Morocco.
Slovakia, who won the King's Cup in Thailand in March, face the Netherlands in Trnava on 31st May and Morocco in Geneva on 4th June.
Viktoria Plzen keeper Matús Kozácik, who started the World Cup qualification campaign as his country's number one, has not been included in the squad, with Dúbravka getting the nod along with Michal Sulla of Slovan Bratislava and Rotherham's Marek Rodak.
Coach Kozák explained: "Rodak is young, talented and playing in England regularly. Kozácik is still available. "Dúbravka has had a fantastic half a season with Newcastle and Sulla convinced me in Thailand; apart from one mistake he did well."
Former Newcastle defender Lubo Satka, who won his first full cap in the Thailand tournament, has also been called up after a strong season in his homeland with FC DAC which saw him named in the Fortuna Liga team of the season.
On Monday, Magpies goalkeeper Matz Sels - who has spent the season on loan with Anderlecht - was named in Belgium's initial squad for the World Cup finals in Russia.