The incident comes just a day after a coconut was lobbed onto the pitch during the Edinburgh derby between Hearts and Hibs.
Fan unrest at Scottish football has seen a worrying upturn this season, with Rangers ace Tavernier himself attacked by a Hibs supporter last month.
Scott Sinclair was nearly hit by a bottle when Celtic played Hibs earlier this season.
David Hamilton, vice-chair of the Scottish Police Federation, recently spoke out about the number of growing incidents at grounds.
“This particular surge correlates with the repeal of the Offensive Behaviour at Football Act,” he said.
James Tavernier was taking a throw for Rangers when the pie incident happened (Image: PA)
It appears as though the centre of the pie had already been eaten (Image: PA)
Rangers won the clash 3-0 (Image: PA)
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Scott Arfield scored a hat-trick for Rangers (Image: PA)
“I think people have been emboldened to behave in ways that are unacceptable.
“The legislation was well-intended, but difficult to enforce. But some people took the repeal of the act to mean they can behave how they want at sports stadia. And the fact is they can’t.
“But my take on it, and our organisation’s take on it, is that this is a football club problem. We really need to see the clubs standing up and dealing with this. If the clubs had dealt with this at the outset then we wouldn’t have had this legislation let alone anything else that has happened since.
Steven Gerrard watched from the stands (Image: GETTY)
A coconut was thrown on the pitch during Hearts vs Hibs on Saturday (Image: BTSPORT)
“People need to look at this and say: ‘This is our problem. How do we fix it?’ The introduction of HD CCTV at Hibs is to be welcomed. But why on earth did they not do that five years ago?
“What price is there on safety? What price is there on conduct? The game is ruining itself. It is ruining it for families. Families are turning their backs on it. It is short-sighted not to invest in this and deal with it as a football problem.”
Rangers won the clash at Fir Park 3-0 thanks to a Scott Arfield hat-trick.
And manager Gerrard watched on from the stands after accepting a one-match touchline ban for criticising the referee after last weekend’s Old Firm defeat to Celtic.