We show that the alteration between intervals of cyclic activity and grand minima like the Maunder minimum in the 17th century, which is characteristic for the long-term variation of the solar activity, can be described as on-off intermittency arising in a dymano driven by the instability of magnetic flux tubes in the overshoot layer below the convection zone. The combination of a threshold in field strength for dynamo action and random fluctuations due to magnetic fields from a turbulent convection zone dynamo leads to activity cycles with strong amplitude variations and the occasional appearance of grand minima of very low activity. The resulting pattern is in qualitative agreement with the long-term records of solar activity.