Three other left-wing officials have also received threatening letters containing bullets.
The Spanish tourism minister Reyes Maroto has received a letter containing "a bloody knife", a senior Socialist official has said.
It is one of a series of threatening parcels that have been sent to left-wing figures, just a few days before crucial regional elections in Madrid.
Last week, the leader of the left-wing Podemos party, Pablo Iglesias, the interior minister and the head of the civil guard received threatening letters. The letters contained bullets from an assault rifle used by the Spanish army between the 1960s and 1980s.
Meanwhile, on Tuesday, the Spanish government said the country's postal service had intercepted another letter containing two bullets, addressed to the conservative president of the Madrid region, Isabel Diaz Ayuso.
Spanish police say they are "investigating these events".
The threats have been "strongly condemned" by Spanish politicians, including Prime Minister Pedro Sanchez.
"Enough of this! We will not allow it. We will not allow hatred to take over coexistence in Spain," Sanchez said on Twitter.
"[We are] neither tolerant nor complicit with violence and the propagation of hatred. Our unreserved condemnation and utmost repulsion against these acts."
Maroto - who is on the Socialist list for the regional election - expressed her thanks for the support of social media and reiterated that “freedom will prevail”.
“Threats and violence will never silence the voice of democracy,” she tweeted.
The police are trying to determine whether the red marks on the knife sent to the Tourism Minister are indeed blood.
Meanwhile Spain’s far-right party Vox had expressed doubts about whether the threats are genuine, which has prompted fresh tension during the election campaign.
Diaz Ayuso is the current front-runner for the May 4 regional elections in Madrid.
The Interior Ministry said they have agreed to reinforce protection measures for those politicians that have been threatened.
The state postal company Correos has also opened a case against a security company that failed to detect the three letters with bullets on 19 April.