Yes, but only if the FSA is a restricted type. According to IRS Publication 969, an employee covered by a high-deductible health plan (HDHP) and a regular, general-purpose health FSA that pays or reimburses qualified medical expenses generally can’t contribute to an HSA, because the FSA counts as other health coverage that pays before the HDHP deductible is met.
The IRS lets you keep making HSA contributions while also covered by a limited-purpose health FSA (which pays only for permitted items such as dental and vision care, plus preventive care) or a post-deductible health FSA (which pays nothing until at least the minimum HDHP deductible is met). A dependent care FSA covers child or elder care, not medical costs, so it does not affect HSA eligibility. One trap: being covered during a general-purpose FSA’s grace period is allowed only if that FSA’s balance at the end of the prior plan year was zero.
Source: IRS Publication 969, Health Savings Accounts and Other Tax-Favored Health Plans (sections “Other employee health plans” and “Health FSA—grace period”).
Image: “52nd MDG Pharmacy”, U.S. Air Force photo by Senior Airman Jessica Sanchez-Chen, public domain, via Wikimedia Commons.