This is a complicated question because the publication history of Doctor Faustus is a complicated one. Our only information on Renaissance Elizabethan plays comes from written and published records. Faustus was first published more than a decade after its first performance and after Marlowe's death, therefore, Marlowe was not on hand to oversee publication.
Another complicating factor is that plays could be altered--lines dropped, scenes added etc--for performances without the playwright's consent. As a result, there is no definitive text of Faustus. Some think the short 1604 Text A version is the authentic version, while others think the longer 1616 Text B version is the authentic version, with all of it composed by Marlowe.
What we do know is that while modern publications divide Faustus into five Acts, neither Text A nor Text B--both in a combination of blank verse and prose--have acts but are divided into scenes only. The 1604 Text A has thirteen scenes and 1485 lines, while the 1616 Text B has twenty scenes and 2125 lines. In summary, though we do not the original form of the play as Marlowe wrote it, we do know that he used no act divisions, only scene divisions.