We report on an RXTE/PCA observation of Aql X-1 during its outburst in March 1997 in which, immediately following a Type-I burst, the broad-band 2-10 keV flux decreased by about 10% and the kilohertz QPO frequency decreased from 813+-3 Hz to 776+-4 Hz. This change in kHz QPO frequency is much larger than expected from a simple extrapolation of a frequency-flux correlation established using data before the burst. Meanwhile a very low frequency noise (VLFN) component in the broad-band FFT power spectra with a fractional root-mean-square (rms) amplitude of 1.2% before the burst ceased to exist after the burst. All these changes were accompanied by a change in the energy spectral shape. If we characterize the energy spectra with a model composed of two blackbody (BB) components and a power law component, almost all the decrease in flux was in the two BB components. We attribute the two BB components to the contributions from a region very near the neutron star or even the neutron star itself and from the accretion disk, respectively.