D'Arnaud was put on the 7-day concussion disabled list last week, retroactive to May 14, and later replaced on the roster by Triple-A C Juan Centeno.
He was cleared by doctors on Thursday and took batting practice Friday.
According to Alderson, in order to come back, d'Arnaud must pass a post-concussion test, which has to be approved by MLB.
D’Arnaud had a light headache after last Tuesday’s game, during which he was hit with a bat on a follow through swing by Alfonso Soriano. Terry Collins said d'Arnaud did not have an immediate reaction, but was still feeling effects from the incident two days later.