They will replace left-arm spinner Enamul Haque junior and batsman Tushar Imran, who were in the Test squad in the recent home series against India.
India won the series 1-0, after the rain-hit first match ended in a draw.
Bangladesh will play three Tests and three one-day matches against Sri Lanka. The Test series begins in Colombo on June 25.
Aftab Ahmed, Tamim Iqbal, Tushar Imran, Farhad Reza and uncapped off-spinner-cum-batsman Mahmudullah Riyad will join the squad before the start of the one-day series.
The Bangladesh Cricket Board will name the one-day squad for the tour later.
Test squad: Mohammad Ashraful (captain), Masharafe Mortaza, Habibul Bashar, Javed Omar, Mehrab Hossain jnr, Shahriar Nafees, Rajin Saleh, Saqibul Hasan, Khaled Mashud (wk), Shahadat Hossain, Syed Rasel, Mohammad Rafique, Abdur Razzak, Mohammad Sharif and Mushfiqur Rahim (stand-by wk). Coach: Shaun Williams.