We report the discovery of a mysterious giant Hα blob that is ~8 kpc away from the main MaNGA target 1-24145, one component of a dry galaxy merger, and has been identified in the first-year SDSS-IV MaNGA data. The size of the Hα blob is ~3–4 kpc in radius, and the Hα distribution is centrally concentrated. However, there is no optical continuum counterpart in the deep broadband images reaching ~26.9 mag arcsec$\mathrm{<mrow\; data-mjx-texclass="ORD">-2</mrow>}$ in surface brightness. We estimate that the masses of the ionized and cold gases are 3.3 x 10$\mathrm{<mrow\; data-mjx-texclass="ORD">5</mrow>}$ M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$ and 1.3 x 10$\mathrm{<mrow\; data-mjx-texclass="ORD">9</mrow>}$ M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$, respectively. The emission-line ratios indicate that the Hα blob is photoionized by a combination of massive young stars and AGNs. Furthermore, the ionization line ratio decreases from MaNGA 1-24145 to the Hα blob, suggesting that the primary ionizing source may come from MaNGA 1-24145, likely a low-activity AGN. Possible explanations for this Hα blob include the AGN outflow, the gas remnant being tidally or ram-pressure stripped from MaNGA 1-24145, or an extremely low surface brightness galaxy. However, the stripping scenario is less favored according to galaxy merger simulations and the morphology of the Hα blob. With the current data, we cannot distinguish whether this Hα blob is ejected gas due to a past AGN outburst, or a special category of "ultra-diffuse galaxy" interacting with MaNGA 1-24145 that further induces the gas inflow to fuel the AGN in MaNGA 1-24145.