National transport spokesman Chris Bishop said Twyford's actions were "anti-democratic and strikes at the heart of what MPs are elected to do".
But over the same 18-month period, Twyford gave the green light to officials meeting with 23 National MPs.
Despite this, Bishop said Twyford was "playing politics".
In a statement, Twyford said plenty of opposition MPs have had meetings with officials and it is taken on a case by case basis – "just like the former government did".
"MPs will always get a full update from NZTA, whether written or otherwise."
He said no one wants NZTA officials tied up in meetings when they have important work to get on with.
Bishop said that all meeting requests from Government MPs have been given Twyford's seal of approval.
The OIA document showed that on four occasions in the last 18 months Twyford approved meetings between officials and Government MPs.