Kitson, a £5.5million summer signing from Reading, was carried off on a stretcher with a knee injury early in the 1-0 victory over West Brom on Saturday while Shawcross was substituted with a back injury.
Both were examined by a specialist on Tuesday and were told to rest for the next few days.
"Dave has opened up the medial ligament in his knee a bit. It's now a case of seeing what rest does for him over the next day or two,'' Pulis told the Stoke Sentinel.
"It's a similar story with Ryan after the scan showed up a couple of what I am told are very small fractures in the back. We are keeping our fingers crossed it is nowhere near as serious as it sounds.
"As with Dave, we won't make any kind of decision on Ryan until we've seen what a couple of days' rest will do for him.''
Both are unlikely to face Hull in Saturday's Premier League match at the Britannia Stadium.