There is little appetite at the FA for charging the 19-year-old for his blast about 'inconsistent' decisions, which he later deleted, but they will consider the comments today.
Red mist: Arsenal's Abou Diaby pushes Kevin Nolan after clashing with Joey Barton
Wilshere, who is expected to start for England in Denmark on Wednesday, posted criticism about Diaby's red card and asked why Nolan was not sent off for a similar offence later on.
It is not viewed as questioning Dowd's integrity in the same way as former Liverpool forward Ryan Babel, who was fined for posting an image of referee Howard Webb in a Manchester United shirt.
Outspoken: Jack Wilshere (left), in action in the draw against Newcastle
Newcastle 4 Arsenal 4: The inside line on the greatest comebackGraham Poll: Nolan and Diaby should have seen red but second Newcastle penalty was baffling
Explore more:People: Jack Wilshere, Ryan Babel Places: Liverpool, United Kingdom, Denmark