The attacks began in southern Kashmir after India's home minister visited the region to review security, a border security force spokesman said.
Indian troops returned fire but one guard was killed and six were injured by a shell fired at the Arnia post in the Jammu region.
At least 100 civilians were being moved from homes in the villages of Arnia and Ramgarh near the frontier, local Indian police said.
While nearly 200 smaller violations of the 2003 ceasefire agreement have been reported this year, the border security force spokesman called the latest skirmishes the most serious in a decade.
Both sides have acknowledged an increase in the number of cross-border attacks since the Pakistani and Indian prime ministers met for their first face-to-face meeting last month in New York and agreed on the need to reduce tensions.