The all-rounder left the squad 'for personal reasons' midway through Sunday's opening day, and the club has confirmed he will not be at Wantage Road for day two.
It means the County will be a batsman down in their first innings against the White Rose, as they look to overhaul the visitors' 158 all out.
It is also not yet know whether or not the former Lancashire man will return for days three and four, but if he does he will be allowed to slot straight back into the team.
A club statement read: "Luke Procter will miss day two of the ongoing LV= Insurance County Championship fixture against Yorkshire.
"Procter left the squad to return home midway through day one for personal reasons.
"The match referee has confirmed Procter will be able to resume his involvement in the fixture with immediate effect on his return to the squad, though at this stage the club are unable to confirm whether he will play any further part in the match."