In order to better understand the mechanism of panel flutter at low supersonic speeds, and to study the viscous effect on flutter boundary and flutter type, a coupled computational fluid dynamics and computational structure dynamics (CFD/CSD) methodology has been adopted. Detailed modal stability analyses have been conducted through the higher-order dynamic mode decomposition (HODMD) method, which has been used to extract dynamic modes from CFD/CSD time-domain data. The results show that at low supersonic speeds, for relatively small dynamic pressure, the stability of the first mode increases due to viscous effect and decreases when the dynamic pressure exceeds a certain critical value. For other higher-order modes the flow viscosity has a stabilizing effect when the dynamic pressure is small, and has a destabilizing when the dynamic pressure exceeds a certain value. The mode stability variation causes the difference of flutter boundary and flutter type between viscous and inviscid solutions at low supersonic speeds. Moreover, it is found that for a simply supported 2D panel, the higher-order single-mode flutter can still occur in the turbulent flow around Mach 1.4 within certain structural parameter values, especially when the mass ratio is small. The high frequency of this type of flutter suggest that more severe structural fatigue problem may occur on simply supported panels with large aspect ratio at certain parameter values, thus requiring due attention.