The game was immediately suspended after the shot stopper came off his line and collided with Ajax striker Bryan Brobbey.
Vaessen stayed lying on the ground after the incident and the referee stopped play and called on the medical staff.
The situation grew more severe as RKC players surrounded the goalkeeper to block fans' view of him while he was being treated.
The 28-year-old was soon taken off and the players were taken down the tunnel as the situation was reviewed.
Shortly afterwards, it was announced that the rest of the game would not go ahead on Saturday.
Later, Frank van Mosselveld, RKC's director, gave a positive update on the stopper, insisting that he was conscious when he left the stadium.
He told reporters: "He regained consciousness and was taken to the hospital. Etienne was out for a while. A big compliment to the medical people who immediately followed the protocol and started resuscitation. It was a shock for the bystanders because then you immediately think it's a heart problem. It doesn't seem like that now.
"Etienne was knocked out for a while. The medical people immediately started resuscitation, but it does not look like a heart problem. When he was taken off the field, he was awake again, but he did not know where he was.
"Obviously this has a huge impact. It was quite a shock. It also looked serious with the sheets and shielding."
After it was confirmed that the game was abandoned, the RKC players returned to the field to applaud their fans.
Some of the home team's players were in tears as they circled the field, with defender Dario van den Buijs in particular distress. The centre-back had to be consoled by ystriker Michiel Kramer and was then seen being hugged by one of the supporters.