Mudbanks (MBs) are a natural phenomenon, forming along the southwest coast of India during southwest monsoon (SWM), almost every year. High waves initiate these formations. The temporal variability (both intra-annual and multi-decadal) of wave climate of the southeastern Arabian Sea (AS) is related to main climate indices which determine climate fluctuations in this region, and based on that, occurrence of MBs is illustrated. Voluntary Observing Ships data and climate indices such as El Niño phenomenon index for the site 5N-5S and 170W-120W (NINO3.4), El Niño/Southern Oscillation (ENSO), Southern Oscillation Index (SOI), Pacific Decadal Oscillation (PDO), AAO, Atlantic Multi-decadal Oscillation (AMO), and IO Dipole (IOD) have been analyzed. Using wavelet correlation method, high correlations with positive and negative phase of climatic indices (IOD, SOI, NINO3.4, ENSO, AMO, PDO, and AAO) fluctuations in heights of wind waves and swell and time lags between them on monthly, yearly, decadal, and multi-decadal time scales are identified. For the first time, high correlation between the annual fluctuations of AMO and monthly average wave heights is shown. It has been found that the El Niño phenomenon plays a major role in the variability of wave climate of the southeastern AS for all time scales. A strong variability in wave climate at short time scales, such as 0.5, 1, 3.0–3.5, 4–5, and 7–8 years, is evident from the analyses. Decadal changes correspond to 10, 12–13, and 16 years. The influence of El Niño is manifested with a delay of several months (3–6) on annual time scales and about 1–2 years on a decadal and multi-decadal time scales. Possible connection between the occurrence of MBs and variability in wave climate in the southeastern AS is shown for the periods 7, 10–12, 18–20, and about 40 years correlating with fluctuation in the climate indices—IOD, ENSO, NINO3.4, and SOI. It is shown that intra-annual fluctuations in occurrence and duration of existence of MBs depend on the distribution of highest monthly averaged significant wave heights (SWHs) in the summer monsoon cycle.