The assimilation of hyperspectral infrared sounders (HIS) observations aboard Earth-observing satellites has become vital to numerical weather prediction, yet this assimilation is predicated on the assumption of clear-sky observations. Using collocated assimilated observations from the Atmospheric Infrared Sounder (AIRS) and the CloudAerosol Lidar with Orthogonal Polarization (CALIOP), it is found that nearly 7.7% of HIS observations assimilated by the Naval Research Laboratory Variational Data Assimilation SystemAccelerated Representer (NAVDAS-AR) are contaminated by cirrus clouds. These contaminating clouds primarily exhibit visible cloud optical depths at 532 nm (COD532nm) below 0.10 and cloud-top temperatures between 240 and 185 K as expected for cirrus clouds. These contamination statistics are consistent with simulations from the Radiative Transfer for TOVS (RTTOV) model showing a cirrus cloud with a COD532nm of 0.10 imparts brightness temperature differences below typical innovation thresholds used by NAVDAS-AR. Using a one-dimensional variational (1DVar) assimilation system coupled with RTTOV for forward and gradient radiative transfer, the analysis temperature and moisture impact of assimilating cirrus-contaminated HIS observations is estimated. Large differences of 2.5 K in temperature and 11 K in dewpoint are possible for a cloud with COD532nm of 0.10 and cloud-top temperature of 210 K. When normalized by the contamination statistics, global differences of nearly 0.11 K in temperature and 0.34 K in dewpoint are possible, with temperature and dewpoint tropospheric root-mean-squared errors (RMSDs) as large as 0.06 and 0.11 K, respectively. While in isolation these global estimates are not particularly concerning, differences are likely much larger in regions with high cirrus frequency.