Since the late 20th century, young star-forming dwarf galaxies with extremelylow heavy-element abundances have been identified in the localuniverse\cite{1972ApJ...173...25S, 1990Natur.343..238I, 2022ApJS..262....3N}.Such a population of galaxies, represented by SBS 0335-052E, is intensivelystudied as a laboratory of galaxy formation, and interpreted as galaxies withhard emission and energetic outflows driven by massivestars\cite{1990Natur.343..238I, 2004ApJ...606..213T, 2009AA...503...61I}. Herewe report the temporal flux variability of SBS 0335-052E in $3-4 \ \mu$m bandson timescale of months to years with dimming and brightening up to 50\% over 12years. This is a clear signature of dust torus emission of an active massiveblack hole in SBS 0335-052E. The deep optical spectrum reveals a very broadcomponent with $1.24\ (\pm 0.01) \times 10^{4}$ km s$^{-1}$ in H$\alpha$emission, suggesting emission originated from broad line regions around themassive black hole. The black hole mass is estimated to be $\sim 100$ thousandsolar masses from the spectral energy distribution. This is the first exampleof the massive black hole existence in a long-considered young star-formingdwarf galaxy.