If it's a repetitive motion, there is the risk of over use injury.
And, btw, pro tour cyclists have been known to have knee issues.
Same with the wannabes and posers in a typical spin class.
Some - but not all - of the more common reasons that cycling (on an actual bicycle or not) can irritate the knees include:
1) Too low of a saddle height. Generally speaking, the pain manifests in irritation at the patellar tendon.
2) Too high of a saddle height. Generally speaking, the pain manifests in irritation at the posterior aspect. This typically has to do with the hamstring complex (and/or the popliteus in some cases).
3) "Mashing" This is when the rider ONLY puts effort into the down stroke. The problem is increased when the rider mashes in too large of a gear.
4) Improper knee tracking. The patella does not track correctly in relation to the foot. Different people have different Q angles and this can result in knee irritation. Just as in squatting, you do NOT want excessive valgus nor varus.
5) Incorrect crank arm length. This is nothing you, the OP, or anyone who "rides" for any length of time on a gym stationary bike has much control over. If it's any consolation, most of the stationary bikes at gyms have cranks that should suffice for the average height adult. It is, however, something to keep in mind should you decide to pursue actual cycling.
6) Incorrect cleat position/pedal design/pedal float. Like #5, this is something that should not concern those who use the typical stationary bikes. So the information is primarily for those looking to get into real cycling.
I currently use the Shimano Dura Ace pedals (Dura Ace is the flagship line from one of the best companies in the world).
And I've also used the top end models from Look (the first company to start the clipless pedal revolution when they used the technology from ski bindings).
To this day, after all those miles, my knees prefer the Time RXS (it has to do with a special design that allows lateral float).
One of the strongest riders I've ever known, however, swears by Speedplays. So the choice is highly individual. The take-home message is pedal selection and the degree of float you choose for the cleats do matter.
6) Not peddling in circles. The first time you see an experienced rider actually pedaling in circles, it's unmistakeable. Everyone else looks like they're pedaling in choppy squares. Not unlike calligraphy, it's something of an art form.
When the foot/pedal is near the 5-6 o'clock position, you want to sweep the foot back. The classic Greg LeMond cue is to pretend you are scraping gum off the bottom of your shoe. This will engage your posterior chain.
As your foot/pedal nears the 9 o'clock position, you want to drive your knee up and forward. This engages your hip flexor complex.
Now, keep in mind that even the smoothest riders turn into mashers when fatigued. The nature of pedaling is such that, when very fatigued, the individual has a much easier time on the down stroke. This explains why when you watch Le Tour or any other high-level race, and those guys are grinding out the final kilometers on those mountain stages, they look less than elegant. But don't believe that they actually pedal that way when fresh.
In order to engage the sweep back and knees up/forward, you'll need to stabilize your feet on the pedals. For the typical stationary bike at the gym, this means actually using those rubber strips that no one else does.
I do not know exactly how you hurt your knee and what you've done since but to answer your question, yes, cycling can and will further irritate injured knees if the individual approaches it in a questionable manner.
And yes, cycling can irritate or even injure those who've never had knee issues if they approach it in a questionable manner. Many a rider or spin class heroine will attest to this; rarely publicly, of course. But that no longer surprises me.
(edited for spelling)