Mourinho has publicly criticised the 21-year-old full-back on a number of occasions, suggesting that the England international lacks the commitment, desire and football intelligence to be a regular in his starting XI.
Relations between the player and manager appear to have thawed after he started last weekend's win over Sunderland, but Le Saux believes that Mourinho has taken a risk with the way he has handled the situation.
"Some people need an arm around them and some need a more confrontational style of manager but it sounds like Luke Shaw is not responding particularly well to public criticism," he told BBC Radio 5 live.
"I think it's a high-risk strategy by Jose. Not only do you shame the player, and if he doesn't react that backfires on you, but also what message does it send out to other players in the that group? It puts people on edge.
"I can't think of many occasions, with anybody I've worked with, where someone has been criticised publicly and it's really paid dividends. You need to be protected if you're finding form hard to find, so it's certainly not a strategy I would promote."
Shaw has made just two Premier League starts for United since October.