The impact of the recession on global markets motivates us to explore the effect of the stock market on the economic stability of a country. The growth of a stock market depends on various factors such as inter-dependency, globalization, economic policies etc. In this paper, we apply the recently developed multifractal detrended partial cross-correlation analysis method on some Asian markets by assuming NASDAQ composite index commonly influences these markets. For this purpose, we analyze the daily returns of three Asian markets such as China’s Shanghai composite index (SHCOMP), Japan’s Nikkei stock average index (NIKKEI 225), and India’s Bombay stock exchange (BSE) sensex index over a period of 18 years (2000–2018). The analysis was performed between all bivariate time series after removing the external influence factor and the results indicate that there exists long-range partial cross-correlation behavior and multifractal nature. For comparison, we also performed analysis without removal of external influence factor i.e. multifractal detrended cross-correlation analysis. From the calculated Hurst scaling exponents, we found that the NASDAQ composite index shows significant influence on these analyzed Asian stock markets.