The fatty acids (FA) present in sheep milk have beneficial compounds, which might prevent cardiovascular diseases. Inulin fiber was added to sheep milk to enhance the prebiotic biological effects to this milk. This study aimed to verify the FA profile, atherogenic (AI) and thrombogenic indices (TI) in prebiotic sheep milk yogurt (PSMY) with added inulin (0, 2, 4 and 6%) during 28 d of storage. Thus, CLA trans-10,cis-12 were detected, but below qualification limit, meaning they were in low amounts in PSMY. The predominant FA were palmitic, oleic, myristic and capric. There was an increase (P < 0.05) of saturated fatty acids (SFA) during storage in PSMY. Therefore, palmitic appeared with approximately 33% (C16:0 and SFA: r = 0.582), myristic with approximately 20% (C14:0 and SFA: r = 0.894) and capric with approximately 16% (C10:0 and SFA: r = 0.929). Oleic acid indicated an antiatherogenic (C18:1n9 and AI: r = −0.845) and antithrombotic (C18:1n9 and TI: r = −0.897) properties and represented around 92% of MUFA. CLA cis-9,trans-11 represented approximately 78% of PUFA and 2% of FA, which indicated that PSMY are a great source of it. There could be a direct link between CLA and oleic acid (r = 0.978), as well CLA increased (P < 0.05) along storage. Still, ALA was present in low levels, corresponding to about 22% of PUFA and 1% FA. There was a drop (P < 0.05) in ALA level at the first storage measure, which was maintained until the last storage measurement. ALA has nutritional importance due to its anti-thrombogenetic effect. PSMY might be considered a food with low atherogenic and thrombogenic risk, because of the low levles of AI and TI. Plus, sheep milk yogurt may have benefitial prebiotic effects with inulin addition.