This study was conducted to determine the availability of micronutrients in soils of Sulaimani Governorate and to evaluate their capacity to sustain agriculture. Soil samples were collected in 10 locations at two depths: 0 to 15 and 15 to 30 cm. Available forms of iron (Fe), zinc (Zn), manganese (Mn), and copper (Cu) were determined using a diethylenetriamine pentaacetic acid extraction, and the corresponding total amounts of these elements were determined in the samples by aqua regia digestion. The geochemical model—PHREEQC—was used to determine the speciation of elements and saturation indices in the studied soils. Physical and chemical parameters were assessed to determine their importance to the availability of these micronutrients. Results for available forms of Fe were lower than the critical range in all the studied locations. In general, there were low amounts of available Fe, Zn, and Mn in the studied soils, although there was a high amount of available Cu. Total concentrations of Fe ranged between 2.93% and 4.12%, Zn between 68 and 122 mg kg−1, Mn between 642 and 1,030 mg kg−1, and Cu between 31 and 64 mg kg−1. Saturation indices showed that many minerals such as aragonite, cuprous ferrite, dolomite, goethite, hematite, lepidocrocite, magnesioferrite, rhodochrosite, and smithsonite were supersaturated or had precipitated in these locations. The high Cu content of these Vertisols makes them suitable for agriculture, provided there is appropriate management of soil and water resources. The major factors affecting micronutrient availability were organic matter content and interaction between elements. Electrical conductivity had a significant positive effect on the availability of Mn, whereas total and active CaCO3 had negative impacts on the availability of Fe, Zn, and Mn in the studied soils.