Most of the time, not.
First, let's clear the air. Despite what some companies would have you believe, there is no standard for a 4K-capable HDMI cable. Most HDMI cables will work with 4K, no matter what.
If you're looking for a cable that gives you a bit more peace of mind, make sure that the cable is labeled "High Speed" and has a speed rating of 10Gbps/sec or higher. This will ensure that it is built for the high transfer rates demanded by 4K, which carries a huge amount of data from point to point.
Don't waste your time with cables that are "specially designed for 4K," as they are usually just a waste of money. However, you should also avoid any cable using a translation technology like Redmere and any devices designed to put HDMI over Ethernet, unless such cables and devices are specifically designed to carry 4K content.