We present low-temperature measurements of the low-frequency $1/f$ noise arising from an ensemble of two-level fluctuators in the oxide barrier of Al/AlO$_{x}$/Al Josephson junctions. The fractional noise power spectrum of the critical-current and normal-state resistance have similar magnitudes and scale linearly with temperature, implying an equivalence between the two. Compiling our results and published data, we deduce the area and temperature scaling of the noise for AlO$_{x}$ barrier junctions. We find that the density of two-level fluctuators in the junction barrier is similar to the typical value in glassy systems. We discuss the implications and consistency with recent qubit experiments.
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