What is the minimum requirement for the dataset for time series forecasting?
Sure! A time-series is just a set of data points indexed temporally, and that's exactly what you have for each patient.

You can certainly build a forecaster using this data.  You may run into a couple wrinkles since your data is not spaced evenly, but that's not an insurmountable barrier.

If you want to quickly prototype a forecasting model, FB Prophet is incredibly easy to use and often works well out-of-the-box.