Possibly. Increasing interest rates means that the risk-free rate of return is going higher. Go back to your Investing 101 college course - as the risk-free rate goes higher, it is going to entice an increasing number of folks to not want to take the higher risk of being in stocks. It doesn't all happen at once, it's gradual. Some are going to be happy to lock in 3% long term. For others, the magic number is going to be 4%. Still others will gradually back away when they can secure 5%. This is exactly the reverse of what took place as rates were pushed to zero - folks who rely on fixed income were getting nothing, so they were forced in to stocks to get their yield. It's worked out extremely well for them. Now, as rates move higher, they can get their fixed income without the market risk.
Stocks have been fully valued for some time now (in my view). At some point the effects of the rising interest rates are going to be putting pressure on the stock market.