The duo both had to be substituted because of injury in last night’s dismal 3-1 defeat at York City.
Webster left the ground wearing a protective boot on his left ankle having collapsed to the ground on the stroke of half-time.
No other player was involved in the incident, with Adam Barton called from the bench to stand in at centre half.
Bennett departed the field in the 66th minute, replaced by Ben Tollitt for a first appearance in five matches.
The winger exited Bootham Crescent on crutches, with his left leg apparently cause for concern.
The full extent of their injuries was unknown in the immediate aftermath of a second-successive defeat.
However, it was a worrying sight to see both leave York in such a manner.
Paul Cook was already without Christian Burgess (ankle) and Gary Roberts (head) for last night’s fixture.
Their presence was sorely missed as the Blues turned in an abject display against a Minstermen side without a win in 12 matches.
Webster had replaced Burgess in the centre of defence for the trip to Bootham Crescent, while Marc McNulty had come in for Roberts.
Now Pompey’s medical team must assess two new casualties during what has turned out to be a desperately disappointing week for the club.
Cook said: ‘We are not sure the full extent at the moment on Kyle and Adam. We’ll know more later.
‘But I have to say, it doesn’t look good.’
The Blues entertain eighth-placed Wycombe on Saturday, now seeking to strengthen their play-off spot.