Miniaturization and integration of optical tweezers are attractive. Optical fiber-based trapping systems allow optical traps to be realized in miniature systems, but the optical traps in these systems lack reliability or mobility. Here, we present the all-fiber modular optical tweezers (AFMOTs), in which an optical trap can be reliably created and freely moved on a sample substrate. Two inclined optical fibers are permanently fixed to a common board, rendering a modular system where fiber alignments are maintained over months. The freely movable optical trap allows particles to be trapped in their native locations. As a demonstration, we applied AFMOTs to trap and deform freely floating individual cells. By the cell mechanical responses, we differentiated the nontumorigenic breast epithelial cell line (MCF10A) from its cancerous PTEN mutants (MCF10 PTEN-/-). To further expand the functionalities, three modalities of AFMOTs are demonstrated by changing the types of fibers for both the optical trap creation and particle position detection. As a miniature and modular system that creates a reliable and mobile optical trap, AFMOTs can find potential applications ranging from point-of-care diagnostics to education, as well as helping transition the optical trapping technology from the research lab to the field.