"The league have received a formal complaint regarding alleged incidents in a Division Two game on Saturday," the league said in a statement on X.
"A full investigation has been initiated and until such time as the formal processes are complete no further comment will be made."
Last week Bowes took eight catches in Saltburn's 22-run win over Shildon Railway. The men's Test record for catches by a keeper in an innings is seven.
Bowes leads the league standings with 31 catches, 10 more than any other player.
Rory Cotterill, who captained Middlesbrough second XI during a 29-run defeat by Saltburn last month, responded to a social media post containing the video and alleged two further incidents of cheating by Saltburn in that match.
The original video of the incident has had more than five million views on X, with publications in Australia and New Zealand among those to report it.
BBC Sport understands a meeting between Saltburn, the league and legal representatives is due to take place on Tuesday night.
Norton declined to comment.
