The 24-year-old came under a shower of missiles as he was carried off on a stretcher after injuring his knee during the north London derby at the Emirates Stadium on January 4.
Stewards and St John Ambulance staff were also hit by the coins, in a confrontation that saw Walcott make a "2-0" gesture with his hands in retaliation, referring to the scoreline in the FA Cup third-round tie.
His knee injury means he will be out of action for six months and will miss out on the World Cup in Brazil with England.
On Monday, Scotland Yard released grainy pictures of the three men suspected of throwing coins.
The force said: "During the match, an Arsenal player on a stretcher, medical staff carrying him and stewards were struck by coins and other missiles thrown at them from a section of the crowd occupied by Tottenham fans.
"The player and stewards received minor injuries as a result. Officers from the Metropolitan Police launched an investigation and have now identified three men they would like to contact."
Anyone with information can call the Public Order Crime Investigation Team on 07769 241315.
In the days after the match, the Football Association confirmed that it had contacted Arsenal and Spurs over the missile-throwing and would back the harshest punishments possible, including life bans.
Police are also investigating anti-Semitic tweets, that referred to the Holocaust, that were posted after the match.