I've had this happen and I never know what causes it. What I do is leave the plant in but mound the soil up above the squeezed part. The plant always seems to recover. It develops new roots above the pinched part.
Dave's advice is the way I would go also. It kind of looks like damping off but the pinched part is up from the soil line and my experience with damping off it has happened very close to the soil line.
It was a weird thing to be sure. The whole seedling was only about 4" tall. And None of the other seedlings planted in the same soil did that. I'm glad no one has diagnosed it as some communicable disease of tomatoes.