Among the objects said to have been hurled from the upper tier of the BT Scotland South Stand was a glass bottle that landed amongst Easter Road fans towards the end of the match, which the Capital club won 3-1 to advance to the final against Celtic next month.
It is understood that Hibs chiefs are aware of the incident and pushing for a full investigation, as well as seeking an explanation as to why supporters of the Ibrox side were sold tickets placing them directly above opposition fans housed in the lower tiers of the South Stand.
One supporter told the Evening News: “I was in section I6 of the South Stand Lower Tier and in the 90th minute, a glass bottle was thrown from the Rangers fans in the section above us.
"Thankfully, and luckily, no one seemed to be injured however it could have caused some serious harm.”
Another Hibs fan wrote on social media that their friend had been hit by a bottle apparently thrown from the upper tier of the main stand while a third claimed a glass bottle thrown from above had bounced off his back before landing and smashing.
Police are already probing an incident during the first half in which objects were thrown at a number of Hibs players as they celebrated Martin Boyle’s third goal while Hibs have also confirmed their own investigation and talks with league chiefs.
Meanwhile, officers in Cambuslang are carrying out enquiries and appealing for the public’s assistance in connection with a disturbance on the M74 motorway.
Video footage posted online appeared to show fans of both Hibs and Rangers brawling at the side of the road while supporter buses were stationary in congested traffic en route to Hampden.
Detective Sergeant Darren Munogee of Cambuslang Police Station said: “We are aware of the videos circulating online and are urging anyone who was on the buses, or driving on the carriageway at the time to contact us.
"We would like to hear from anyone who has footage of the disturbance as this will assist our investigation.”