According to islamqa it is not part of the sunnah to say this - meaning that this is not a ma'thur dua or dhikr. However this phrase is essentially just supplicating to Allah using His names which is prescribed.
ولله الأسماء الحسنى فادعوه بها
And to Allah belong the best names, so invoke Him by them.
— Quran 7:180
And part of that is to call upon Allah with those of His names which are appropriate to the situation, as demonstrated in the following ma'thur duas:
أذهب الباس رب الناس، اشف وأنت الشافي لا شفاء إلا شفاؤك، شفاء لا يغادر سقما
Take away the disease, O the Lord of the people! Cure him as You are the One Who cures. There is no cure but Yours, a cure that leaves no disease.
فاغفر لي مغفرة من عندك، وارحمني إنك أنت الغفور الرحيم
Bestow on me a forgiveness from You, and Have Mercy on me, You are the Forgiver, the Merciful