BT Sport changed plans for the pair to attend Ibrox ahead of the Europa League double header featuring both Glasgow clubs.
The broadcaster instead had Stiliyan Petrov in a studio to analyse Celtic's early-evening encounter with Real Betis in Spain ahead of Rangers' later clash with Lyon in Glasgow.
Sutton wrote on Twitter: "I'm not allowed to work on the Celtic game tonight from a studio at Ibrox along with Neil Lennon as Stewart Robertson the Rangers CEO says we are a security risk. Good to see Rangers ground breaking diversity and inclusion campaign 'Everyone Anyone' is working well…"
A BT Sport spokesman added: "We had hoped that Darrell Currie and the team would be able to present the coverage of both the Celtic and Rangers UEFA Europa League games live from Ibrox this evening, as we have done in the past.
"Rangers have since raised security concerns and so we have had to change our plans."
Rangers insisted they had complied with competition rules.
A statement read: "We have complied with all UEFA contractual obligations to facilitate BT as host broadcaster. Any conjecture or speculation is both inaccurate and unhelpful."