Dendritic cells serve a key function in host defence, linking innate detection of microbes to activation of pathogen-specific adaptive immune responses. Whether there is cell-intrinsic recognition of human immunodeficiency virus (HIV) by host innate pattern-recognition receptors and subsequent coupling to antiviral T-cell responses is not yet known. Dendritic cells are largely resistant to infection with HIV-1, but facilitate infection of co-cultured T-helper cells through a process of trans-enhancement. Here we show that, when dendritic cell resistance to infection is circumvented, HIV-1 induces dendritic cell maturation, an antiviral type I interferon response and activation of T cells. This innate response is dependent on the interaction of newly synthesized HIV-1 capsid with cellular cyclophilin A (CYPA) and the subsequent activation of the transcription factor IRF3. Because the peptidylprolyl isomerase CYPA also interacts with HIV-1 capsid to promote infectivity, our results indicate that capsid conformation has evolved under opposing selective pressures for infectivity versus furtiveness. Thus, a cell-intrinsic sensor for HIV-1 exists in dendritic cells and mediates an antiviral immune response, but it is not typically engaged owing to the absence of dendritic cell infection. The virulence of HIV-1 may be related to evasion of this response, the manipulation of which may be necessary to generate an effective HIV-1 vaccine.