Tierney is an 18-year-old defender who has been playing consistently for the Scottish Premiership giants in recent weeks.
The teenager is enjoying a breakthrough season at the Bhoys, but former Celtic midfielder and manager Hay believes that he will find himself out of the starting lineup soon.
“One other player at Celtic who will find himself out of the team soon enough is Kieran Tierney,” the 67-year-old wrote in The Glasgow Evening Times.
“The 18-year-old has been absolutely brilliant for Celtic and within a few matches has gone from being not even on the bench to first choice left-back, especially in Europe.”
“But like all young players, he will have to be handled carefully. That means sooner rather than later being taken out of the firing line, so to speak,” added Hay.
“When that happens, Tierney I am sure will accept that is part of his football development and work hard in training so he is ready when the manager calls on him again. That is the only thing to do in such circumstances. “
Celtic are on course to winning the Scottish Premiership title this season. The Hoops are at the top of the league table at the moment with 39 points from 16 matches.
Ronny Deila’s side are as many as seven points clear of second-place Aberdeen, and the title is now theirs to lose.
Celtic, who defeated Inverness Caledonian Thistle 3-1 away from home last weekend, will take on Hamilton Academical at Celtic Park in the Scottish Premiership on Saturday afternoon.
Hamilton are fifth in the league standings at the moment with 22 points from 16 matches.