Interband cascade infrared photodetectors (ICIPs) potentially offer mid-wave infrared detection at very high operating temperatures due to their nearly ideal photovoltaic operation. An ICIP typically makes use of several cascade stages grown in series, each of which consists of an active absorption region with a mid-wave cutoff wavelength, an intra-band relaxation region for electron transport and an inter-band tunneling region to enable electron transport to the next stage. The latter two also effectively act as a hole-barrier (hB) and an electron-barrier (eB), respectively, forming a preferential path for each carrier. Here, an ICIP with a relatively large eB was investigated. One of the key parameters to measure for detector performance is the noise spectrum, particularly to observe the behavior at low frequencies where the noise is often much larger than estimates based on the ideal shot noise expression would predict. This paper presents the results of noise spectrum measurements of differently sized ICIP devices, taken using an external trans-impedance amplifier with a cooled, internal impedance converter and a cooled feedback resistor. Measurements were taken at different operating temperatures and voltage biases in order to determine the noise-dependence on each.