Hi, I'm 24 years old and have been feeling the same thing for the past 24 hours in my left foot! The vibration sensation lasts maybe one second, and goes away for about 5 seconds. I can feel it only when my foot is resting on something, such as the floor, my other foot, my bed when I was trying to fall asleep - I don't necessarily need to be putting any weight on it, but I find that I don't feel it unless I am physically touching something with my foot. It really does feel just like a phone vibrating on silent. I'm a medical student and when I googled this strange symptom the first thing I came across mentioned a brain tumour - I don't think this is something to freak out about!
Like many other people I can also relate this to a particularly bad case of stress - I've been stressed with exams for the past couple of months and this past week (which included Christmas and consequently family dramas) I've overloaded myself with a large dose of extra stress.
I have noticed today that while I was distracted from this stress (far away from it), it went away (I purposely sat down to see if it was happening, and it went away for a good 6 hours at least). When I was "re-exposed" to a source (person) of stress, it came back! I have a feeling that this might be psychosomatic (meaning that it's a physical manifestation of a psychological or emotional problem) - it isn' the first time I have had something like this, although I have never had this specific vibration sensation.
Going by the amount of people who have reported feeling this, and how young they are, I'd just like to offer my two cents of "medical student" opinion and say that this might be a very common thing that doesn't mean anything terrible - maybe try to identify what triggers this feeling (such as a particular worry, thought, situation) and let your doctor know that you are concerned, but don't panic. If this doesn't go away or I find anything out I will re-post!