Assalaamu'Alaikum WarahmatUllahe Wabarakatuho
I failed to find that who initially constructed that Masjid. But it was in Bani Salma, and All I found is that Our Prophet Muhammad S.A.W offered Zuhr Salat in Bani Salma Masjid and about the event. And some how its structure is given that how it was in that time. Then later on in 893 Hijri it was reconstructed or repaired and shelter was changed by Shaheen Aljamali. It is also said that till Sultan Sulaiman Al-'Esani time the building was there, and in 950 Hijri he constructed it again from start. Then after that it is written that AbulAziz aal saud then extended its Courtyard, built stairs, and a Minara (Tower) for Azan.
Allah Knows Best