As a result of topping Group D, the Blues avoided potential matches against holders Barcelona or eight-time champions Lyon, as they look to send Emma Hayes out on a high in her final season in charge.
Chelsea will instead travel to take on Ajax in the first leg on March 19/20, with the return fixture a week later at Stamford Bridge.
Should the Blues get the job done, they will play either Barcelona or SK Brann in the semi-finals.
Hayes' side were unbeaten in the group stage, picking up 14 points from their six matches as they booked their place in the knockout stages with time to spare.
Victory over Real Madrid at Stamford Bridge secured top spot, and formed part of what is now an eight-match winning run across all competitions.
Ajax finished second in Group C, behind PSG only on goal difference, to reach the quarter-finals of the Champions League for the first time.
Chelsea are eyeing a first European title, having regularly come close in recent seasons. The Blues were beaten by Barcelona in the final three years ago, and have on three occasions since 2018 suffered semi-final defeats.
They were edged out 2-1 on aggregate at the last-four stage last season, and a repeat of that fixture is on the cards should both clubs come through their quarter-final ties.