The former Ukraine international feels the 28-year-old would be making a huge mistake if he decided to leave the Spanish capital, particularly with Carlo Ancelotti now in charge
It has been reported the Portugal international is considering a return to Manchester United, but Shevchenko believes the 28-year-old attacker would be foolish to quit Madrid.
"I do not know why Cristiano would want to go," the former AC Milan striker told AS. "When you're in Madrid, you must stay in Madrid.
"We would all like to have played there. I do not think you can go much further in your career."
Shevchenko says Ronaldo would be better to remain at the Bernabeu in order to have the opportunity to work with Madrid's new boss, Carlo Ancelotti, whom the former Ukraine forward played under during his time at San Siro.
"I'm sure Ancelotti will be a friend to all, not just Cristiano Ronaldo, and open doors for everyone in that dressing room," he added.
"He will shake up Real, but in a good way, like a breath of fresh air. I am sure he will want to convince Cristiano to stay and be the best.
"I do not think there are too many teams as suitable for Carlo's type and style of play as Real Madrid. It's good for both parties. They are made for each other."
Ancelotti has arrived at Madrid from Paris Saint-Germain, whom he last season led to a first Ligue 1 success since 1994.