Police Sergeant Major Narong Pitisit, 45, died of injuries sustained in the clash with opposition protesters at the Thai-Japanese Stadium, where candidates were filing their nominations for the February 2 elections.
Medical officials said he was shot in the chest and suffered severe blood loss.
Erawan Emergency Centre said 48 protesters and some police men were injured.
In a statement, the EC said its recommendation to delay the polls was due to the violence that started after police fired teargas and rubber bullets at stone-throwing mobs trying to enter the stadium.
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The opposition Democrat Party has said it will boycott the polls while caretaker Premier Yingluck Shinawatra has insisted the elections will be held as scheduled.
The protesters want Yingluck to quit and have demanded the polls be delayed, vowing to disrupt them.
This morning, demonstrators, some armed with sling shots, threw rocks while trying to storm the stadium where 27 political parties were involved in drawing of lots. Police responded with teargas and fired rubber bullets.
Deputy Prime Minister and Foreign Minister Surapong Tovichakchaikul, who also heads CAPO, said police had shown full restraint in dealing with the protesters who had the right to demonstrate their opposition.
However, the government and police could no longer tolerate their illegal actions as the country had laws that should be respected by all, he said adding the handling of the situation met international standards.
The protesters have been demanding Yingluck's resignation since mid-October. The protests began after the government tried to introduce an amnesty bill that would have paved the way for the return of her brother, former premier Thaksin Shinawatra currently in self-exile in Dubai.