Citrus fiber is recognized to be a structuring ingredient that can form particle hydrogels (in water) or emulgels (oil droplets entrapped in the water phase). Emulgels are used in a wide range of food applications, such as low-fat and low-calorie foods or food supplements, since they are particularly suitable for the delivery of bioactive molecules. In the present work, emulgels containing citrus fiber that are potentially suitable as a food supplement of curcumin were produced by high-speed homogenization and using two different edible oils: Miglyol® 812N and rice oil (both at 0.4 w/w). The viscoelasticity of the emulgels and single phases (hydrogels and oil phases) was investigated by frequency sweep test in the linear region, and was previously determined by a stress sweep test. The consistency, in terms of complex shear modulus (G*), of both the hydrogel and emulgels increased more than linearly with increasing fiber fractions (from 0.020 w/w to 0.030 w/w), whereas the structuring degree, in terms of phase angle (δ), was almost independent of the fiber fraction. The addition of curcumin does not affect the viscoelasticity of oil phases based on either oil. The emulgel with rice oil showed higher G* than that containing Miglyol® 812N, but they showed similar δ values. Rheological results for the emulgels were modelled using the weak gel model. The gel strength increases with increasing fiber fraction; network extension seems independent from fiber concentration. Curcumin does not change the consistency of emulgels, but it slightly decreases teir structure extension (δ moves from 5.5° to approximately 7.0°), According to in vitro diffusion studies, the diffused curcumin percentage (Cur%) at 24 h was 14.6% for the emulgel with Miglyol® 812N, whereas for the emulgel with rice oil, it was 18.3%. These results can be considered promising for making future investigations attractive for the development of edible emulsions for food supplementation of curumin.