Since you are using pandas, you can do something like this:
import pandas as pd
import matplotlib.pyplot as plt
pd.np.random.seed(1234)
idx = pd.date_range(end=datetime.today().date(), periods=10, freq='D')
vals = pd.Series(pd.np.random.randint(1, 10, size=idx.size), index=idx)
vals.iloc[4:8] = pd.np.nan
print vals
Here is an example column from a DataFrame with DatetimeIndex
2016-03-29 4.0
2016-03-30 7.0
2016-03-31 6.0
2016-04-01 5.0
2016-04-02 NaN
2016-04-03 NaN
2016-04-04 NaN
2016-04-05 NaN
2016-04-06 9.0
2016-04-07 1.0
Freq: D, dtype: float64
To build it without dates where the data is NaN, you can do something like this:
fig, ax = plt.subplots()
ax.plot(range(vals.dropna().size), vals.dropna())
ax.set_xticklabels(vals.dropna().index.date.tolist());
fig.autofmt_xdate()
What should produce such a plot:

, matplotlib, .plot.
, , .
.autofmt_xdate(), .